LMFDB - Embedded newform 637.2.x.b.80.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.2
Character	$\chi$	$=$	637.80
Dual form			637.2.x.b.215.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433802 - 1.61897i) q^{2} +0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(-0.520288 + 1.94174i) q^{5} +(1.03250 - 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +O(q^{10})$	\(q+(-0.433802 - 1.61897i) q^{2} +0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(-0.520288 + 1.94174i) q^{5} +(1.03250 - 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +3.36932 q^{10} +(0.694217 + 0.694217i) q^{11} +(-0.258049 - 0.446954i) q^{12} +(-1.60977 + 3.22624i) q^{13} +(-1.23834 - 0.331813i) q^{15} +(-2.48181 + 4.29862i) q^{16} +(2.99281 + 5.18370i) q^{17} +(-1.12497 - 4.19844i) q^{18} +(-1.98532 - 1.98532i) q^{19} +(-0.421043 - 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 - 1.49448i) q^{23} +(0.900016 - 0.900016i) q^{24} +(0.830467 + 0.479471i) q^{25} +(5.92151 + 1.20663i) q^{26} +3.56710i q^{27} +(3.65708 + 6.33425i) q^{29} +2.14878i q^{30} +(8.34708 - 2.23659i) q^{31} +(4.18037 + 1.12013i) q^{32} +(-0.442736 + 0.442736i) q^{33} +(7.09397 - 7.09397i) q^{34} +(-1.81745 + 1.04931i) q^{36} +(4.63309 - 1.24143i) q^{37} +(-2.35294 + 4.07541i) q^{38} +(-2.05753 - 1.02663i) q^{39} +(3.47451 - 2.00601i) q^{40} +(-0.886060 + 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.767427 - 0.205631i) q^{44} +(-1.34925 + 5.03547i) q^{45} +(-1.29661 + 4.83903i) q^{46} +(2.96429 + 0.794280i) q^{47} +(-2.74144 - 1.58277i) q^{48} +(0.415990 - 1.55250i) q^{50} +(-3.30589 + 1.90866i) q^{51} +(-0.177238 - 2.91241i) q^{52} +(-3.16223 + 5.47715i) q^{53} +(5.77504 - 1.54742i) q^{54} +(-1.70918 + 0.986797i) q^{55} +(1.26614 - 1.26614i) q^{57} +(8.66852 - 8.66852i) q^{58} +(0.491481 + 0.131692i) q^{59} +(1.00213 - 0.268520i) q^{60} -13.0284i q^{61} +(-7.24196 - 12.5434i) q^{62} +2.67342i q^{64} +(-5.42698 - 4.80434i) q^{65} +(0.908836 + 0.524717i) q^{66} +(0.606011 - 0.606011i) q^{67} +(-4.19491 - 2.42193i) q^{68} +(0.953100 - 1.65082i) q^{69} +(-3.01121 - 11.2380i) q^{71} +(-3.65973 - 3.65973i) q^{72} +(-0.377014 - 1.40704i) q^{73} +(-4.01968 - 6.96230i) q^{74} +(-0.305782 + 0.529629i) q^{75} +(2.19469 + 0.588064i) q^{76} +(-0.769526 + 3.77644i) q^{78} +(5.80137 + 10.0483i) q^{79} +(-7.05555 - 7.05555i) q^{80} +5.50492 q^{81} +5.73802 q^{82} +(-1.23779 - 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(-0.374999 + 1.39951i) q^{86} +(-4.03966 + 2.33230i) q^{87} -1.95941i q^{88} +(2.07729 + 7.75255i) q^{89} +8.73759 q^{90} +2.41881 q^{92} +(1.42638 + 5.32334i) q^{93} -5.14367i q^{94} +(4.88792 - 2.82204i) q^{95} +(-0.714359 + 2.66602i) q^{96} +(-12.0756 + 3.23566i) q^{97} +(1.80030 + 1.80030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.433802	−	1.61897i	−0.306744	−	1.14479i	−0.931433	−	0.363912i	$-0.881441\pi$
$2$	−0.433802	−	1.61897i	−0.306744	−	1.14479i	0.624689	−	0.780873i	$-0.285226\pi$
$3$			0.637748i			0.368204i	0.982907	+	0.184102i	$0.0589377\pi$
$3$			0.637748i			0.368204i	−0.982907	+	0.184102i	$0.941062\pi$
$4$	−0.700831	+	0.404625i	−0.350416	+	0.202313i
$5$	−0.520288	+	1.94174i	−0.232680	+	0.868373i	0.746501	+	0.665384i	$0.231732\pi$
$5$	−0.520288	+	1.94174i	−0.232680	+	0.868373i	−0.979181	+	0.202989i	$0.934934\pi$
$6$	1.03250	−	0.276656i	0.421515	−	0.112945i
$7$		0			0
$7$		0			0
$8$	−1.41124	−	1.41124i	−0.498948	−	0.498948i
$9$	2.59328			0.864426
$10$	3.36932			1.06547
$11$	0.694217	+	0.694217i	0.209314	+	0.209314i	0.803976	−	0.594662i	$-0.202714\pi$
$11$	0.694217	+	0.694217i	0.209314	+	0.209314i	−0.594662	+	0.803976i	$0.702714\pi$
$12$	−0.258049	−	0.446954i	−0.0744924	−	0.129025i
$13$	−1.60977	+	3.22624i	−0.446471	+	0.894798i
$13$	−1.60977	+	3.22624i	−0.446471	+	0.894798i
$14$		0			0
$15$	−1.23834	−	0.331813i	−0.319739	−	0.0856737i
$16$	−2.48181	+	4.29862i	−0.620452	+	1.07465i
$17$	2.99281	+	5.18370i	0.725863	+	1.25723i	0.958618	+	0.284696i	$0.0918925\pi$
$17$	2.99281	+	5.18370i	0.725863	+	1.25723i	−0.232755	+	0.972535i	$0.574774\pi$
$18$	−1.12497	−	4.19844i	−0.265158	−	0.989582i
$19$	−1.98532	−	1.98532i	−0.455464	−	0.455464i	0.441699	−	0.897163i	$-0.354376\pi$
$19$	−1.98532	−	1.98532i	−0.455464	−	0.455464i	−0.897163	+	0.441699i	$0.854376\pi$
$20$	−0.421043	−	1.57135i	−0.0941481	−	0.351366i
$21$		0			0
$22$	0.822765	−	1.42507i	0.175414	−	0.303826i
$23$	−2.58851	−	1.49448i	−0.539742	−	0.311620i	0.205233	−	0.978713i	$-0.434205\pi$
$23$	−2.58851	−	1.49448i	−0.539742	−	0.311620i	−0.744974	+	0.667093i	$0.767538\pi$
$24$	0.900016	−	0.900016i	0.183715	−	0.183715i
$25$	0.830467	+	0.479471i	0.166093	+	0.0958941i
$26$	5.92151	+	1.20663i	1.16130	+	0.236639i
$27$			3.56710i			0.686489i
$28$		0			0
$29$	3.65708	+	6.33425i	0.679103	+	1.17624i	0.975251	+	0.221099i	$0.0709645\pi$
$29$	3.65708	+	6.33425i	0.679103	+	1.17624i	−0.296148	+	0.955142i	$0.595702\pi$
$30$			2.14878i			0.392312i
$31$	8.34708	−	2.23659i	1.49918	−	0.401704i	0.586354	−	0.810055i	$-0.300563\pi$
$31$	8.34708	−	2.23659i	1.49918	−	0.401704i	0.912825	+	0.408351i	$0.133896\pi$
$32$	4.18037	+	1.12013i	0.738992	+	0.198012i
$33$	−0.442736	+	0.442736i	−0.0770704	+	0.0770704i
$34$	7.09397	−	7.09397i	1.21661	−	1.21661i
$35$		0			0
$36$	−1.81745	+	1.04931i	−0.302908	+	0.174884i
$37$	4.63309	−	1.24143i	0.761675	−	0.204090i	0.142984	−	0.989725i	$-0.454330\pi$
$37$	4.63309	−	1.24143i	0.761675	−	0.204090i	0.618690	+	0.785635i	$0.287664\pi$
$38$	−2.35294	+	4.07541i	−0.381697	+	0.661119i
$39$	−2.05753	−	1.02663i	−0.329468	−	0.164393i
$40$	3.47451	−	2.00601i	0.549369	−	0.317178i
$41$	−0.886060	+	3.30682i	−0.138379	+	0.516439i	0.861582	+	0.507619i	$0.169474\pi$
$41$	−0.886060	+	3.30682i	−0.138379	+	0.516439i	−0.999961	+	0.00881984i	$0.997193\pi$
$42$		0			0
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	0.441830	−	0.897099i	$-0.354329\pi$
$43$	−0.748633	−	0.432224i	−0.114165	−	0.0659135i	−0.555995	+	0.831185i	$0.687663\pi$
$44$	−0.767427	−	0.205631i	−0.115694	−	0.0310001i
$45$	−1.34925	+	5.03547i	−0.201134	+	0.750644i
$46$	−1.29661	+	4.83903i	−0.191175	+	0.713476i
$47$	2.96429	+	0.794280i	0.432387	+	0.115858i	0.468446	−	0.883492i	$-0.344814\pi$
$47$	2.96429	+	0.794280i	0.432387	+	0.115858i	−0.0360596	+	0.999350i	$0.511481\pi$
$48$	−2.74144	−	1.58277i	−0.395692	−	0.228453i
$49$		0			0
$50$	0.415990	−	1.55250i	0.0588299	−	0.219556i
$51$	−3.30589	+	1.90866i	−0.462918	+	0.267266i
$52$	−0.177238	−	2.91241i	−0.0245784	−	0.403878i
$53$	−3.16223	+	5.47715i	−0.434366	+	0.752344i	−0.997244	−	0.0741963i	$-0.976361\pi$
$53$	−3.16223	+	5.47715i	−0.434366	+	0.752344i	0.562878	+	0.826540i	$0.309694\pi$
$54$	5.77504	−	1.54742i	0.785883	−	0.210577i
$55$	−1.70918	+	0.986797i	−0.230466	+	0.133060i
$56$		0			0
$57$	1.26614	−	1.26614i	0.167704	−	0.167704i
$58$	8.66852	−	8.66852i	1.13823	−	1.13823i
$59$	0.491481	+	0.131692i	0.0639854	+	0.0171448i	0.290670	−	0.956823i	$-0.406122\pi$
$59$	0.491481	+	0.131692i	0.0639854	+	0.0171448i	−0.226684	+	0.973968i	$0.572789\pi$
$60$	1.00213	−	0.268520i	0.129374	−	0.0346657i
$61$		−	13.0284i		−	1.66811i	−0.551679	−	0.834057i	$-0.686012\pi$
$61$		−	13.0284i		−	1.66811i	0.551679	−	0.834057i	$-0.313988\pi$
$62$	−7.24196	−	12.5434i	−0.919729	−	1.59302i
$63$		0			0
$64$			2.67342i			0.334178i
$65$	−5.42698	−	4.80434i	−0.673134	−	0.595905i
$66$	0.908836	+	0.524717i	0.111870	+	0.0645882i
$67$	0.606011	−	0.606011i	0.0740361	−	0.0740361i	−0.669119	−	0.743155i	$-0.733328\pi$
$67$	0.606011	−	0.606011i	0.0740361	−	0.0740361i	0.743155	+	0.669119i	$0.233328\pi$
$68$	−4.19491	−	2.42193i	−0.508707	−	0.293702i
$69$	0.953100	−	1.65082i	0.114740	−	0.198735i
$70$		0			0
$71$	−3.01121	−	11.2380i	−0.357365	−	1.33370i	−0.877482	−	0.479609i	$-0.840778\pi$
$71$	−3.01121	−	11.2380i	−0.357365	−	1.33370i	0.520117	−	0.854095i	$-0.325888\pi$
$72$	−3.65973	−	3.65973i	−0.431304	−	0.431304i
$73$	−0.377014	−	1.40704i	−0.0441262	−	0.164681i	0.940347	−	0.340217i	$-0.110501\pi$
$73$	−0.377014	−	1.40704i	−0.0441262	−	0.164681i	−0.984473	+	0.175536i	$0.943834\pi$
$74$	−4.01968	−	6.96230i	−0.467279	−	0.809350i
$75$	−0.305782	+	0.529629i	−0.0353086	+	0.0611563i
$76$	2.19469	+	0.588064i	0.251748	+	0.0674556i
$77$		0			0
$78$	−0.769526	+	3.77644i	−0.0871316	+	0.427597i
$79$	5.80137	+	10.0483i	0.652705	+	1.13052i	0.982464	+	0.186454i	$0.0596994\pi$
$79$	5.80137	+	10.0483i	0.652705	+	1.13052i	−0.329758	+	0.944065i	$0.606967\pi$
$80$	−7.05555	−	7.05555i	−0.788834	−	0.788834i
$81$	5.50492			0.611657
$82$	5.73802			0.633658
$83$	−1.23779	−	1.23779i	−0.135865	−	0.135865i	0.635904	−	0.771768i	$-0.280628\pi$
$83$	−1.23779	−	1.23779i	−0.135865	−	0.135865i	−0.771768	+	0.635904i	$0.780628\pi$
$84$		0			0
$85$	−11.6225	+	3.11424i	−1.26064	+	0.337787i
$86$	−0.374999	+	1.39951i	−0.0404372	+	0.150914i
$87$	−4.03966	+	2.33230i	−0.433097	+	0.250049i
$88$		−	1.95941i		−	0.208874i
$89$	2.07729	+	7.75255i	0.220192	+	0.821769i	0.984274	+	0.176649i	$0.0565258\pi$
$89$	2.07729	+	7.75255i	0.220192	+	0.821769i	−0.764082	+	0.645120i	$0.776807\pi$
$90$	8.73759			0.921023
$91$		0			0
$92$	2.41881			0.252179
$93$	1.42638	+	5.32334i	0.147909	+	0.552004i
$94$		−	5.14367i		−	0.530529i
$95$	4.88792	−	2.82204i	0.501490	−	0.289535i
$96$	−0.714359	+	2.66602i	−0.0729090	+	0.272100i
$97$	−12.0756	+	3.23566i	−1.22609	+	0.328531i	−0.813058	−	0.582183i	$-0.802199\pi$
$97$	−12.0756	+	3.23566i	−1.22609	+	0.328531i	−0.413037	+	0.910714i	$0.635532\pi$
$98$		0			0
$99$	1.80030	+	1.80030i	0.180937	+	0.180937i
$100$	−0.776023			−0.0776023
$101$	−7.99635			−0.795667			−0.397833	−	0.917458i	$-0.630238\pi$
$101$	−7.99635			−0.795667			−0.397833	+	0.917458i	$0.630238\pi$
$102$	4.52417	+	4.52417i	0.447959	+	0.447959i
$103$	−5.16928	−	8.95345i	−0.509344	−	0.882210i	−0.999941	−	0.0108235i	$-0.996555\pi$
$103$	−5.16928	−	8.95345i	−0.509344	−	0.882210i	0.490597	−	0.871386i	$-0.336779\pi$
$104$	6.82477	−	2.28122i	0.669224	−	0.223692i
$105$		0			0
$106$	10.2391	+	2.74356i	0.994511	+	0.266479i
$107$	−6.52593	+	11.3032i	−0.630885	+	1.09273i	0.356486	+	0.934301i	$0.383975\pi$
$107$	−6.52593	+	11.3032i	−0.630885	+	1.09273i	−0.987371	+	0.158425i	$0.949358\pi$
$108$	−1.44334	−	2.49994i	−0.138885	−	0.240557i
$109$	−3.03074	−	11.3109i	−0.290292	−	1.08339i	−0.944885	−	0.327403i	$-0.893826\pi$
$109$	−3.03074	−	11.3109i	−0.290292	−	1.08339i	0.654592	−	0.755982i	$-0.272840\pi$
$110$	2.33904	+	2.33904i	0.223019	+	0.223019i
$111$	0.791721	+	2.95474i	0.0751468	+	0.280452i
$112$		0			0
$113$	4.05748	−	7.02777i	0.381696	−	0.661117i	−0.609609	−	0.792702i	$-0.708674\pi$
$113$	4.05748	−	7.02777i	0.381696	−	0.661117i	0.991305	+	0.131586i	$0.0420069\pi$
$114$	−2.59909	−	1.50058i	−0.243427	−	0.140543i
$115$	4.24866	−	4.24866i	0.396189	−	0.396189i
$116$	−5.12600	−	2.95950i	−0.475937	−	0.274782i
$117$	−4.17459	+	8.36653i	−0.385941	+	0.773486i
$118$		−	0.852822i		−	0.0785086i
$119$		0			0
$120$	1.27933	+	2.21587i	0.116786	+	0.202280i
$121$		−	10.0361i		−	0.912375i
$122$	−21.0926	+	5.65174i	−1.90963	+	0.511684i
$123$	−2.10892	−	0.565083i	−0.190155	−	0.0509518i
$124$	−4.94491	+	4.94491i	−0.444066	+	0.444066i
$125$	−8.47036	+	8.47036i	−0.757612	+	0.757612i
$126$		0			0
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	−0.165977	−	0.986130i	$-0.553078\pi$
$127$	6.81853	−	3.93668i	0.605047	−	0.349324i	0.771024	+	0.636805i	$0.219745\pi$
$128$	12.6889	−	3.39999i	1.12155	−	0.300519i
$129$	0.275650	−	0.477440i	0.0242696	−	0.0420362i
$130$	−5.42385	+	10.8702i	−0.475703	+	0.953384i
$131$	−17.2856	+	9.97987i	−1.51025	+	0.871945i	−0.510325	+	0.859982i	$0.670475\pi$
$131$	−17.2856	+	9.97987i	−1.51025	+	0.871945i	−0.999928	+	0.0119634i	$0.996192\pi$
$132$	0.131141	−	0.489425i	0.0114144	−	0.0425990i
$133$		0			0
$134$	−1.24400	−	0.718226i	−0.107466	−	0.0620452i
$135$	−6.92639	−	1.85592i	−0.596129	−	0.159732i
$136$	3.09187	−	11.5390i	0.265125	−	0.989461i
$137$	−2.78324	+	10.3872i	−0.237788	+	0.887437i	0.739084	+	0.673613i	$0.235259\pi$
$137$	−2.78324	+	10.3872i	−0.237788	+	0.887437i	−0.976872	+	0.213824i	$0.931408\pi$
$138$	−3.08608	−	0.826913i	−0.262705	−	0.0703915i
$139$	14.1096	+	8.14616i	1.19676	+	0.690949i	0.959831	−	0.280579i	$-0.0905264\pi$
$139$	14.1096	+	8.14616i	1.19676	+	0.690949i	0.236927	+	0.971527i	$0.423860\pi$
$140$		0			0
$141$	−0.506551	+	1.89047i	−0.0426593	+	0.159207i
$142$	−16.8877	+	9.75012i	−1.41719	+	0.818212i
$143$	−3.35724	+	1.12218i	−0.280747	+	0.0938413i
$144$	−6.43601	+	11.1475i	−0.536334	+	0.928959i
$145$	−14.2022	+	3.80547i	−1.17943	+	0.316027i
$146$	−2.11440	+	1.22075i	−0.174989	+	0.101030i
$147$		0			0
$148$	−2.74470	+	2.74470i	−0.225613	+	0.225613i
$149$	13.2274	−	13.2274i	1.08363	−	1.08363i	0.0874634	−	0.996168i	$-0.472124\pi$
$149$	13.2274	−	13.2274i	1.08363	−	1.08363i	0.996168	−	0.0874634i	$-0.0278761\pi$
$150$	0.990103	+	0.265297i	0.0808416	+	0.0216614i
$151$	0.0351934	−	0.00943004i	0.00286400	−	0.000767406i	−0.257387	−	0.966308i	$-0.582861\pi$
$151$	0.0351934	−	0.00943004i	0.00286400	−	0.000767406i	0.260251	+	0.965541i	$0.416195\pi$
$152$			5.60353i			0.454506i
$153$	7.76118	+	13.4428i	0.627454	+	1.08678i
$154$		0			0
$155$			17.3715i			1.39532i
$156$	1.85738	−	0.113033i	0.148710	−	0.00904988i
$157$	6.22554	+	3.59432i	0.496852	+	0.286858i	0.727413	−	0.686200i	$-0.240723\pi$
$157$	6.22554	+	3.59432i	0.496852	+	0.286858i	−0.230560	+	0.973058i	$0.574056\pi$
$158$	13.7512	−	13.7512i	1.09399	−	1.09399i
$159$	−3.49304	−	2.01671i	−0.277016	−	0.159935i
$160$	−4.34999	+	7.53441i	−0.343897	+	0.595647i
$161$		0			0
$162$	−2.38804	−	8.91230i	−0.187622	−	0.700216i
$163$	−11.6359	−	11.6359i	−0.911397	−	0.911397i	0.0849855	−	0.996382i	$-0.472916\pi$
$163$	−11.6359	−	11.6359i	−0.911397	−	0.911397i	−0.996382	+	0.0849855i	$0.972916\pi$
$164$	−0.717044	−	2.67605i	−0.0559918	−	0.208964i
$165$	−0.629328	−	1.09003i	−0.0489932	−	0.0848586i
$166$	−1.46699	+	2.54090i	−0.113860	+	0.197212i
$167$	−6.49344	−	1.73991i	−0.502478	−	0.134638i	−0.00132801	−	0.999999i	$-0.500423\pi$
$167$	−6.49344	−	1.73991i	−0.502478	−	0.134638i	−0.501150	+	0.865361i	$0.667089\pi$
$168$		0			0
$169$	−7.81725	−	10.3870i	−0.601327	−	0.799003i
$170$	10.0837	+	17.4656i	0.773388	+	1.33955i
$171$	−5.14849	−	5.14849i	−0.393715	−	0.393715i
$172$	0.699554			0.0533405
$173$	−9.51731			−0.723587			−0.361794	−	0.932258i	$-0.617836\pi$
$173$	−9.51731			−0.723587			−0.361794	+	0.932258i	$0.617836\pi$
$174$	5.52834	+	5.52834i	0.419102	+	0.419102i
$175$		0			0
$176$	−4.70709	+	1.26126i	−0.354810	+	0.0950711i
$177$	−0.0839864	+	0.313441i	−0.00631280	+	0.0235597i
$178$	11.6500	−	6.72614i	0.873206	−	0.504146i
$179$		−	6.00707i		−	0.448989i	−0.974475	−	0.224495i	$-0.927927\pi$
$179$		−	6.00707i		−	0.448989i	0.974475	−	0.224495i	$-0.0720731\pi$
$180$	−1.09188	−	4.07496i	−0.0813841	−	0.303729i
$181$	−6.05960			−0.450407			−0.225203	−	0.974312i	$-0.572305\pi$
$181$	−6.05960			−0.450407			−0.225203	+	0.974312i	$0.572305\pi$
$182$		0			0
$183$	8.30883			0.614207
$184$	1.54394	+	5.76207i	0.113821	+	0.424786i
$185$			9.64216i			0.708905i
$186$	7.99956	−	4.61855i	0.586556	−	0.338648i
$187$	−1.52095	+	5.67627i	−0.111223	+	0.415090i
$188$	−2.39886	+	0.642771i	−0.174955	+	0.0468789i
$189$		0			0
$190$	−6.68919	−	6.68919i	−0.485285	−	0.485285i
$191$	21.6273			1.56490			0.782449	−	0.622715i	$-0.213970\pi$
$191$	21.6273			1.56490			0.782449	+	0.622715i	$0.213970\pi$
$192$	−1.70497			−0.123046
$193$	6.85258	+	6.85258i	0.493260	+	0.493260i	0.909332	−	0.416072i	$-0.136594\pi$
$193$	6.85258	+	6.85258i	0.493260	+	0.493260i	−0.416072	+	0.909332i	$0.636594\pi$
$194$	10.4769	+	18.1465i	0.752195	+	1.30284i
$195$	3.06396	−	3.46105i	0.219415	−	0.247851i
$196$		0			0
$197$	−4.47322	−	1.19859i	−0.318704	−	0.0853964i	0.0959210	−	0.995389i	$-0.469420\pi$
$197$	−4.47322	−	1.19859i	−0.318704	−	0.0853964i	−0.414624	+	0.909993i	$0.636087\pi$
$198$	2.13366	−	3.69560i	0.151632	−	0.262635i
$199$	−10.7801	−	18.6717i	−0.764182	−	1.32360i	−0.940678	−	0.339300i	$-0.889810\pi$
$199$	−10.7801	−	18.6717i	−0.764182	−	1.32360i	0.176496	−	0.984301i	$-0.443524\pi$
$200$	−0.495341	−	1.84864i	−0.0350259	−	0.130718i
$201$	0.386483	+	0.386483i	0.0272604	+	0.0272604i
$202$	3.46883	+	12.9459i	0.244066	+	0.910868i
$203$		0			0
$204$	1.54458	−	2.67530i	0.108142	−	0.187308i
$205$	−5.95998	−	3.44100i	−0.416263	−	0.240330i
$206$	−12.2529	+	12.2529i	−0.853702	+	0.853702i
$207$	−6.71272	−	3.87559i	−0.466566	−	0.269372i
$208$	−9.87322	−	14.9267i	−0.684585	−	1.03498i
$209$		−	2.75649i		−	0.190670i
$210$		0			0
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	0.999945	+	0.0105352i	$0.00335353\pi$
$211$	7.39505	+	12.8086i	0.509096	+	0.881780i	−0.490848	+	0.871245i	$0.663313\pi$
$212$		−	5.11807i		−	0.351511i
$213$	7.16701	−	1.92039i	0.491076	−	0.131583i
$214$	21.1306	+	5.66192i	1.44446	+	0.387041i
$215$	1.22877	−	1.22877i	0.0838015	−	0.0838015i
$216$	5.03404	−	5.03404i	0.342523	−	0.342523i
$217$		0			0
$218$	−16.9972	+	9.81336i	−1.15120	+	0.664644i
$219$	0.897335	−	0.240440i	0.0606363	−	0.0162474i
$220$	0.798566	−	1.38316i	0.0538393	−	0.0932524i
$221$	−21.5416	+	1.31094i	−1.44904	+	0.0881832i
$222$	4.44019	−	2.56355i	0.298006	−	0.172054i
$223$	5.52568	−	20.6221i	0.370027	−	1.38096i	−0.490450	−	0.871469i	$-0.663168\pi$
$223$	5.52568	−	20.6221i	0.370027	−	1.38096i	0.860477	−	0.509490i	$-0.170166\pi$
$224$		0			0
$225$	2.15363	+	1.24340i	0.143575	+	0.0828933i
$226$	−13.1379	−	3.52029i	−0.873919	−	0.234166i
$227$	−3.49849	+	13.0566i	−0.232203	+	0.866594i	0.747186	+	0.664615i	$0.231404\pi$
$227$	−3.49849	+	13.0566i	−0.232203	+	0.866594i	−0.979390	+	0.201980i	$0.935262\pi$
$228$	−0.375037	+	1.39966i	−0.0248374	+	0.0926946i
$229$	6.94692	+	1.86142i	0.459066	+	0.123006i	0.480938	−	0.876755i	$-0.340296\pi$
$229$	6.94692	+	1.86142i	0.459066	+	0.123006i	−0.0218726	+	0.999761i	$0.506963\pi$
$230$	−8.72153	−	5.03538i	−0.575081	−	0.332023i
$231$		0			0
$232$	3.77813	−	14.1002i	0.248046	−	0.925721i
$233$	−20.0959	+	11.6024i	−1.31653	+	0.760097i	−0.983168	−	0.182702i	$-0.941515\pi$
$233$	−20.0959	+	11.6024i	−1.31653	+	0.760097i	−0.333359	+	0.942800i	$0.608182\pi$
$234$	15.3561	+	3.12912i	1.00386	+	0.204557i
$235$	−3.08457	+	5.34264i	−0.201215	+	0.348515i
$236$	−0.397731	+	0.106572i	−0.0258901	+	0.00693723i
$237$	−6.40827	+	3.69982i	−0.416262	+	0.240329i
$238$		0			0
$239$	−2.77302	+	2.77302i	−0.179372	+	0.179372i	−0.791082	−	0.611710i	$-0.790482\pi$
$239$	−2.77302	+	2.77302i	−0.179372	+	0.179372i	0.611710	+	0.791082i	$0.290482\pi$
$240$	4.49966	−	4.49966i	0.290452	−	0.290452i
$241$	−3.08037	−	0.825382i	−0.198424	−	0.0531675i	0.158238	−	0.987401i	$-0.449419\pi$
$241$	−3.08037	−	0.825382i	−0.198424	−	0.0531675i	−0.356662	+	0.934233i	$0.616085\pi$
$242$	−16.2482	+	4.35369i	−1.04447	+	0.279866i
$243$			14.2121i			0.911704i
$244$	5.27161	+	9.13070i	0.337480	+	0.584533i
$245$		0			0
$246$			3.65941i			0.233316i
$247$	9.60104	−	3.20920i	0.610900	−	0.204197i
$248$	−14.9361	−	8.62336i	−0.948443	−	0.547584i
$249$	0.789397	−	0.789397i	0.0500260	−	0.0500260i
$250$	17.3877	+	10.0388i	1.09970	+	0.634910i
$251$	5.89697	−	10.2138i	0.372213	−	0.644692i	−0.617692	−	0.786420i	$-0.711932\pi$
$251$	5.89697	−	10.2138i	0.372213	−	0.644692i	0.989906	+	0.141727i	$0.0452656\pi$
$252$		0			0
$253$	−0.759496	−	2.83448i	−0.0477491	−	0.178202i
$254$	−9.33127	−	9.33127i	−0.585496	−	0.585496i
$255$	−1.98610	−	7.41224i	−0.124375	−	0.464173i
$256$	−8.33554	−	14.4376i	−0.520971	−	0.902349i
$257$	8.34519	−	14.4543i	0.520559	−	0.901634i	−0.479156	−	0.877730i	$-0.659057\pi$
$257$	8.34519	−	14.4543i	0.520559	−	0.901634i	0.999714	−	0.0239041i	$-0.00760964\pi$
$258$	−0.892538	−	0.239155i	−0.0555670	−	0.0148891i
$259$		0			0
$260$	5.74735	+	1.17114i	0.356436	+	0.0726310i
$261$	9.48383	+	16.4265i	0.587034	+	1.01677i
$262$	23.6557	+	23.6557i	1.46145	+	1.46145i
$263$	9.51537			0.586743			0.293371	−	0.955999i	$-0.405223\pi$
$263$	9.51537			0.586743			0.293371	+	0.955999i	$0.405223\pi$
$264$	1.24961			0.0769083
$265$	−8.98993	−	8.98993i	−0.552247	−	0.552247i
$266$		0			0
$267$	−4.94418	+	1.32479i	−0.302579	+	0.0810758i
$268$	−0.179504	+	0.669919i	−0.0109650	+	0.0409218i
$269$	−0.275945	+	0.159317i	−0.0168247	+	0.00971373i	−0.508389	−	0.861128i	$-0.669759\pi$
$269$	−0.275945	+	0.159317i	−0.0168247	+	0.00971373i	0.491564	+	0.870841i	$0.336425\pi$
$270$			12.0187i			0.731437i
$271$	−6.94654	−	25.9248i	−0.421972	−	1.57482i	−0.770447	−	0.637504i	$-0.779967\pi$
$271$	−6.94654	−	25.9248i	−0.421972	−	1.57482i	0.348475	−	0.937318i	$-0.386700\pi$
$272$	−29.7103			−1.80145
$273$		0			0
$274$	18.0239			1.08886
$275$	0.243668	+	0.909381i	0.0146937	+	0.0548378i
$276$			1.54259i			0.0928532i
$277$	13.1218	−	7.57587i	0.788412	−	0.455190i	−0.0509909	−	0.998699i	$-0.516238\pi$
$277$	13.1218	−	7.57587i	0.788412	−	0.455190i	0.839403	+	0.543509i	$0.182905\pi$
$278$	7.06764	−	26.3768i	0.423889	−	1.58198i
$279$	21.6463	−	5.80010i	1.29593	−	0.347243i
$280$		0			0
$281$	5.40600	+	5.40600i	0.322495	+	0.322495i	0.849724	−	0.527228i	$-0.176769\pi$
$281$	5.40600	+	5.40600i	0.322495	+	0.322495i	−0.527228	+	0.849724i	$0.676769\pi$
$282$	3.28036			0.195343
$283$	1.79244			0.106549			0.0532746	−	0.998580i	$-0.483034\pi$
$283$	1.79244			0.106549			0.0532746	+	0.998580i	$0.483034\pi$
$284$	6.65752	+	6.65752i	0.395051	+	0.395051i
$285$	1.79975	+	3.11726i	0.106608	+	0.184651i
$286$	3.27315	+	4.94848i	0.193546	+	0.292610i
$287$		0			0
$288$	10.8409	+	2.90480i	0.638803	+	0.171167i
$289$	−9.41380	+	16.3052i	−0.553753	+	0.959128i
$290$	12.3219	+	21.3422i	0.723567	+	1.25325i
$291$	−2.06353	−	7.70122i	−0.120967	−	0.451453i
$292$	0.833545	+	0.833545i	0.0487796	+	0.0487796i
$293$	−6.85691	−	25.5903i	−0.400585	−	1.49500i	−0.812055	−	0.583580i	$-0.801651\pi$
$293$	−6.85691	−	25.5903i	−0.400585	−	1.49500i	0.411471	−	0.911423i	$-0.365015\pi$
$294$		0			0
$295$	−0.511424	+	0.885812i	−0.0297762	+	0.0515739i
$296$	−8.29035	−	4.78644i	−0.481867	−	0.278206i
$297$	−2.47634	+	2.47634i	−0.143692	+	0.143692i
$298$	−27.1529	−	15.6767i	−1.57292	−	0.908127i
$299$	8.98846	−	5.94538i	0.519816	−	0.343830i
$300$		−	0.494908i		−	0.0285735i
$301$		0			0
$302$	−0.0305339	−	0.0528863i	−0.00175703	−	0.00304327i
$303$		−	5.09966i		−	0.292968i
$304$	13.4613	−	3.60695i	0.772059	−	0.206873i
$305$	25.2978	+	6.77851i	1.44855	+	0.388136i
$306$	18.3966	−	18.3966i	1.05166	−	1.05166i
$307$	1.54710	−	1.54710i	0.0882978	−	0.0882978i	−0.661578	−	0.749876i	$-0.730113\pi$
$307$	1.54710	−	1.54710i	0.0882978	−	0.0882978i	0.749876	+	0.661578i	$0.230113\pi$
$308$		0			0
$309$	5.71005	−	3.29670i	0.324833	−	0.187543i
$310$	28.1240	−	7.53581i	1.59734	−	0.428005i
$311$	14.6672	−	25.4043i	0.831699	−	1.44055i	−0.0649904	−	0.997886i	$-0.520702\pi$
$311$	14.6672	−	25.4043i	0.831699	−	1.44055i	0.896690	−	0.442660i	$-0.145965\pi$
$312$	1.45484	+	4.35249i	0.0823644	+	0.246411i
$313$	24.2354	−	13.9923i	1.36987	−	0.790893i	0.378957	−	0.925414i	$-0.376283\pi$
$313$	24.2354	−	13.9923i	1.36987	−	0.790893i	0.990911	+	0.134521i	$0.0429497\pi$
$314$	3.11844	−	11.6382i	0.175984	−	0.656781i
$315$		0			0
$316$	−8.13157	−	4.69476i	−0.457436	−	0.264101i
$317$	−7.59654	−	2.03549i	−0.426664	−	0.114324i	0.0390957	−	0.999235i	$-0.487552\pi$
$317$	−7.59654	−	2.03549i	−0.426664	−	0.114324i	−0.465760	+	0.884911i	$0.654219\pi$
$318$	−1.74970	+	6.52998i	−0.0981185	+	0.366183i
$319$	−1.85854	+	6.93616i	−0.104058	+	0.388350i
$320$	−5.19109	−	1.39095i	−0.290191	−	0.0777564i
$321$	−7.20862	−	4.16190i	−0.402346	−	0.232295i
$322$		0			0
$323$	4.34961	−	16.2330i	0.242019	−	0.903227i
$324$	−3.85802	+	2.22743i	−0.214334	+	0.123746i
$325$	−2.88375	+	1.90745i	−0.159962	+	0.105806i
$326$	−13.7905	+	23.8859i	−0.763788	+	1.32292i
$327$	7.21349	−	1.93285i	0.398907	−	0.106887i
$328$	5.91716	−	3.41627i	0.326720	−	0.188632i
$329$		0			0
$330$	−1.49172	+	1.49172i	−0.0821165	+	0.0821165i
$331$	11.5133	−	11.5133i	0.632826	−	0.632826i	−0.315950	−	0.948776i	$-0.602323\pi$
$331$	11.5133	−	11.5133i	0.632826	−	0.632826i	0.948776	+	0.315950i	$0.102323\pi$
$332$	1.36832	+	0.366640i	0.0750963	+	0.0201220i
$333$	12.0149	−	3.21938i	0.658411	−	0.176421i
$334$			11.2675i			0.616529i
$335$	0.861417	+	1.49202i	0.0470642	+	0.0815176i
$336$		0			0
$337$			11.0114i			0.599827i	0.953966	+	0.299913i	$0.0969578\pi$
$337$			11.0114i			0.599827i	−0.953966	+	0.299913i	$0.903042\pi$
$338$	−13.4252	+	17.1618i	−0.730233	+	0.933480i
$339$	4.48195	+	2.58765i	0.243426	+	0.140542i
$340$	6.88532	−	6.88532i	0.373409	−	0.373409i
$341$	7.34737	+	4.24200i	0.397882	+	0.229717i
$342$	−6.10183	+	10.5687i	−0.329949	+	0.571488i
$343$		0			0
$344$	0.446530	+	1.66647i	0.0240753	+	0.0898501i
$345$	2.70957	+	2.70957i	0.145879	+	0.145879i
$346$	4.12863	+	15.4082i	0.221956	+	0.828352i
$347$	−2.36362	−	4.09391i	−0.126886	−	0.219772i	0.795583	−	0.605845i	$-0.207165\pi$
$347$	−2.36362	−	4.09391i	−0.126886	−	0.219772i	−0.922468	+	0.386073i	$0.873831\pi$
$348$	1.88741	−	3.26910i	0.101176	−	0.175242i
$349$	22.4353	+	6.01151i	1.20093	+	0.321789i	0.803198	−	0.595712i	$-0.203130\pi$
$349$	22.4353	+	6.01151i	1.20093	+	0.321789i	0.397734	+	0.917501i	$0.369797\pi$
$350$		0			0
$351$	−11.5083	−	5.74223i	−0.614269	−	0.306498i
$352$	2.12447	+	3.67970i	0.113235	+	0.196128i
$353$	9.29908	+	9.29908i	0.494940	+	0.494940i	0.909859	−	0.414919i	$-0.136190\pi$
$353$	9.29908	+	9.29908i	0.494940	+	0.494940i	−0.414919	+	0.909859i	$0.636190\pi$
$354$	0.543886			0.0289072
$355$	23.3880			1.24130
$356$	−4.59271	−	4.59271i	−0.243413	−	0.243413i
$357$		0			0
$358$	−9.72526	+	2.60588i	−0.513996	+	0.137725i
$359$	2.43301	−	9.08010i	0.128409	−	0.479229i	−0.871529	−	0.490344i	$-0.836871\pi$
$359$	2.43301	−	9.08010i	0.128409	−	0.479229i	0.999938	+	0.0111144i	$0.00353790\pi$
$360$	9.01037	−	5.20214i	0.474888	−	0.274177i
$361$		−	11.1170i		−	0.585105i
$362$	2.62867	+	9.81032i	0.138160	+	0.515619i
$363$	6.40052			0.335940
$364$		0			0
$365$	2.92826			0.153272
$366$	−3.60439	−	13.4518i	−0.188404	−	0.703135i
$367$			7.31961i			0.382081i	0.981582	+	0.191040i	$0.0611861\pi$
$367$			7.31961i			0.382081i	−0.981582	+	0.191040i	$0.938814\pi$
$368$	12.8484	−	7.41801i	0.669767	−	0.386690i
$369$	−2.29780	+	8.57550i	−0.119619	+	0.446423i
$370$	15.6104	−	4.18279i	0.811544	−	0.217453i
$371$		0			0
$372$	−3.15361	−	3.15361i	−0.163507	−	0.163507i
$373$	−1.08512			−0.0561856			−0.0280928	−	0.999605i	$-0.508943\pi$
$373$	−1.08512			−0.0561856			−0.0280928	+	0.999605i	$0.508943\pi$
$374$	9.84951			0.509306
$375$	−5.40196	−	5.40196i	−0.278956	−	0.278956i
$376$	−3.06241	−	5.30425i	−0.157932	−	0.273546i
$377$	−26.3229	+	1.60191i	−1.35570	+	0.0825025i
$378$		0			0
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.454119	−	0.890941i	$-0.650046\pi$
$379$	−25.1695	−	6.74414i	−1.29287	−	0.346423i	−0.838749	+	0.544518i	$0.816713\pi$
$380$	−2.28374	+	3.95555i	−0.117153	+	0.202915i
$381$	2.51061	+	4.34851i	0.128623	+	0.222781i
$382$	−9.38197	−	35.0140i	−0.480023	−	1.79147i
$383$	−3.76918	−	3.76918i	−0.192596	−	0.192596i	0.604221	−	0.796817i	$-0.293484\pi$
$383$	−3.76918	−	3.76918i	−0.192596	−	0.192596i	−0.796817	+	0.604221i	$0.793484\pi$
$384$	2.16834	+	8.09234i	0.110652	+	0.412961i
$385$		0			0
$386$	8.12146	−	14.0668i	0.413372	−	0.715981i
$387$	−1.94141	−	1.12088i	−0.0986876	−	0.0569773i
$388$	7.15375	−	7.15375i	0.363177	−	0.363177i
$389$	−2.97841	−	1.71958i	−0.151011	−	0.0871864i	0.422590	−	0.906321i	$-0.361121\pi$
$389$	−2.97841	−	1.71958i	−0.151011	−	0.0871864i	−0.573602	+	0.819134i	$0.694454\pi$
$390$	−6.93249	−	3.45905i	−0.351040	−	0.175156i
$391$		−	17.8907i		−	0.904773i
$392$		0			0
$393$	−6.36465	−	11.0239i	−0.321054	−	0.556082i
$394$			7.76196i			0.391042i
$395$	−22.5295	+	6.03677i	−1.13358	+	0.303743i
$396$	−1.99015	−	0.533259i	−0.100009	−	0.0267973i
$397$	−0.424872	+	0.424872i	−0.0213237	+	0.0213237i	−0.717688	−	0.696365i	$-0.754800\pi$
$397$	−0.424872	+	0.424872i	−0.0213237	+	0.0213237i	0.696365	+	0.717688i	$0.254800\pi$
$398$	−25.5525	+	25.5525i	−1.28083	+	1.28083i
$399$		0			0
$400$	−4.12212	+	2.37991i	−0.206106	+	0.118995i
$401$	−11.5834	+	3.10377i	−0.578448	+	0.154995i	−0.536168	−	0.844111i	$-0.680129\pi$
$401$	−11.5834	+	3.10377i	−0.578448	+	0.154995i	−0.0422800	+	0.999106i	$0.513462\pi$
$402$	0.458047	−	0.793361i	0.0228453	−	0.0395693i
$403$	−6.22113	+	30.5301i	−0.309896	+	1.52081i
$404$	5.60409	−	3.23553i	0.278814	−	0.160973i
$405$	−2.86414	+	10.6891i	−0.142320	+	0.531147i
$406$		0			0
$407$	4.07819	+	2.35454i	0.202148	+	0.116710i
$408$	7.35898	+	1.97183i	0.364324	+	0.0976203i
$409$	3.00424	−	11.2120i	0.148550	−	0.554396i	−0.851022	−	0.525131i	$-0.824016\pi$
$409$	3.00424	−	11.2120i	0.148550	−	0.554396i	0.999572	−	0.0292657i	$-0.00931689\pi$
$410$	−2.98542	+	11.1418i	−0.147440	+	0.550252i
$411$	−6.62441	−	1.77501i	−0.326758	−	0.0875546i
$412$	7.24558	+	4.18324i	0.356964	+	0.206093i
$413$		0			0
$414$	−3.36248	+	12.5489i	−0.165257	+	0.616747i
$415$	3.04747	−	1.75946i	0.149594	−	0.0863683i
$416$	−10.3432	+	11.6837i	−0.507119	+	0.572842i
$417$	−5.19520	+	8.99836i	−0.254410	+	0.440651i
$418$	−4.46267	+	1.19577i	−0.218276	+	0.0584870i
$419$	30.9881	−	17.8910i	1.51387	−	0.874032i	0.513999	−	0.857791i	$-0.328164\pi$
$419$	30.9881	−	17.8910i	1.51387	−	0.874032i	0.999868	−	0.0162408i	$-0.00516982\pi$
$420$		0			0
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	−0.786646	−	0.617404i	$-0.788184\pi$
$421$	−3.47255	+	3.47255i	−0.169242	+	0.169242i	0.617404	+	0.786646i	$0.288184\pi$
$422$	17.5288	−	17.5288i	0.853287	−	0.853287i
$423$	7.68723	+	2.05979i	0.373766	+	0.100150i
$424$	12.1922	−	3.26690i	0.592107	−	0.158655i
$425$			5.73985i			0.278424i
$426$	−6.21813	−	10.7701i	−0.301269	−	0.521814i
$427$		0			0
$428$		−	10.5622i		−	0.510544i
$429$	−0.715668	−	2.14108i	−0.0345528	−	0.103372i
$430$	−2.52239	−	1.45630i	−0.121640	−	0.0702291i
$431$	0.347144	−	0.347144i	0.0167213	−	0.0167213i	−0.698697	−	0.715418i	$-0.746236\pi$
$431$	0.347144	−	0.347144i	0.0167213	−	0.0167213i	0.715418	+	0.698697i	$0.246236\pi$
$432$	−15.3336	−	8.85286i	−0.737739	−	0.425934i
$433$	−8.89347	+	15.4039i	−0.427393	+	0.740266i	−0.996641	−	0.0818999i	$-0.973901\pi$
$433$	−8.89347	+	15.4039i	−0.427393	+	0.740266i	0.569248	+	0.822166i	$0.307235\pi$
$434$		0			0
$435$	−2.42693	−	9.05744i	−0.116363	−	0.434271i
$436$	6.70070	+	6.70070i	0.320905	+	0.320905i
$437$	2.17201	+	8.10604i	0.103901	+	0.387764i
$438$	−0.778531	−	1.34846i	−0.0371997	−	0.0644317i
$439$	−14.3012	+	24.7704i	−0.682559	+	1.18223i	0.291639	+	0.956529i	$0.405800\pi$
$439$	−14.3012	+	24.7704i	−0.682559	+	1.18223i	−0.974197	+	0.225698i	$0.927534\pi$
$440$	3.80467	+	1.01946i	0.181381	+	0.0486008i
$441$		0			0
$442$	11.4672	+	34.3065i	0.545437	+	1.63179i
$443$	3.68575	+	6.38391i	0.175115	+	0.303309i	0.940201	−	0.340620i	$-0.110637\pi$
$443$	3.68575	+	6.38391i	0.175115	+	0.303309i	−0.765086	+	0.643928i	$0.777304\pi$
$444$	−1.75043	−	1.75043i	−0.0830716	−	0.0830716i
$445$	−16.1342			−0.764836
$446$	−35.7837			−1.69441
$447$	8.43576	+	8.43576i	0.398998	+	0.398998i
$448$		0			0
$449$	22.5220	−	6.03476i	1.06288	−	0.284798i	0.315315	−	0.948987i	$-0.397890\pi$
$449$	22.5220	−	6.03476i	1.06288	−	0.284798i	0.747565	+	0.664189i	$0.231223\pi$
$450$	1.07878	−	4.02606i	0.0508541	−	0.189790i
$451$	−2.91077	+	1.68053i	−0.137063	+	0.0791332i
$452$			6.56704i			0.308887i
$453$	0.00601399	+	0.0224445i	0.000282562	+	0.00105454i
$454$	22.6558			1.06329
$455$		0			0
$456$	−3.57364			−0.167351
$457$	−1.16783	−	4.35841i	−0.0546289	−	0.203878i	0.933217	−	0.359313i	$-0.116989\pi$
$457$	−1.16783	−	4.35841i	−0.0546289	−	0.203878i	−0.987846	+	0.155435i	$0.950322\pi$
$458$		−	12.0544i		−	0.563263i
$459$	−18.4908	+	10.6757i	−0.863076	+	0.498297i
$460$	−1.25848	+	4.69671i	−0.0586769	+	0.218985i
$461$	−32.1809	+	8.62285i	−1.49882	+	0.401606i	−0.912703	−	0.408623i	$-0.866009\pi$
$461$	−32.1809	+	8.62285i	−1.49882	+	0.401606i	−0.586112	+	0.810230i	$0.699342\pi$
$462$		0			0
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.883028	+	0.469321i	$0.155501\pi$
$463$	29.0991	+	29.0991i	1.35235	+	1.35235i	0.469321	+	0.883028i	$0.344499\pi$
$464$	−36.3047			−1.68540
$465$	−11.0787			−0.513761
$466$	27.5016	+	27.5016i	1.27399	+	1.27399i
$467$	2.85866	+	4.95135i	0.132283	+	0.229121i	0.924556	−	0.381045i	$-0.124436\pi$
$467$	2.85866	+	4.95135i	0.132283	+	0.229121i	−0.792273	+	0.610167i	$0.791103\pi$
$468$	−0.459626	−	7.55267i	−0.0212462	−	0.349122i
$469$		0			0
$470$	9.98767	+	2.67619i	0.460697	+	0.123443i
$471$	−2.29227	+	3.97033i	−0.105622	+	0.182943i
$472$	−0.507749	−	0.879447i	−0.0233710	−	0.0404798i
$473$	−0.219657	−	0.819771i	−0.0100998	−	0.0376931i
$474$	8.76981	+	8.76981i	0.402811	+	0.402811i
$475$	−0.696841	−	2.60065i	−0.0319733	−	0.119326i
$476$		0			0
$477$	−8.20054	+	14.2038i	−0.375477	+	0.650345i
$478$	5.69239	+	3.28650i	0.260364	+	0.150321i
$479$	23.5643	−	23.5643i	1.07668	−	1.07668i	0.0798746	−	0.996805i	$-0.474548\pi$
$479$	23.5643	−	23.5643i	1.07668	−	1.07668i	0.996805	−	0.0798746i	$-0.0254520\pi$
$480$	−4.80506	−	2.77420i	−0.219320	−	0.126624i
$481$	−3.45307	+	16.9459i	−0.157446	+	0.772665i
$482$			5.34507i			0.243461i
$483$		0			0
$484$	4.06087	+	7.03363i	0.184585	+	0.319711i
$485$		−	25.1312i		−	1.14115i
$486$	23.0089	−	6.16522i	1.04371	−	0.279660i
$487$	14.6038	+	3.91309i	0.661763	+	0.177319i	0.574041	−	0.818826i	$-0.305375\pi$
$487$	14.6038	+	3.91309i	0.661763	+	0.177319i	0.0877214	+	0.996145i	$0.472041\pi$
$488$	−18.3862	+	18.3862i	−0.832303	+	0.832303i
$489$	7.42080	−	7.42080i	0.335580	−	0.335580i
$490$		0			0
$491$	−3.79911	+	2.19342i	−0.171451	+	0.0989875i	−0.583270	−	0.812278i	$-0.698227\pi$
$491$	−3.79911	+	2.19342i	−0.171451	+	0.0989875i	0.411819	+	0.911266i	$0.364894\pi$
$492$	1.70664	−	0.457294i	0.0769415	−	0.0206164i
$493$	−21.8899	+	37.9144i	−0.985871	+	1.70758i
$494$	−9.36056	−	14.1516i	−0.421151	−	0.636713i
$495$	−4.43238	+	2.55904i	−0.199221	+	0.115020i
$496$	−11.1016	+	41.4317i	−0.498476	+	1.86034i
$497$		0			0
$498$	−1.62045	−	0.935569i	−0.0726142	−	0.0419238i
$499$	−19.3575	−	5.18682i	−0.866560	−	0.232194i	−0.201960	−	0.979394i	$-0.564731\pi$
$499$	−19.3575	−	5.18682i	−0.866560	−	0.232194i	−0.664599	+	0.747200i	$0.731398\pi$
$500$	2.50897	−	9.36361i	0.112205	−	0.418753i
$501$	1.10963	−	4.14118i	0.0495745	−	0.185014i
$502$	−19.0940	−	5.11623i	−0.852209	−	0.228349i
$503$	0.917016	+	0.529439i	0.0408877	+	0.0236065i	0.520305	−	0.853981i	$-0.325818\pi$
$503$	0.917016	+	0.529439i	0.0408877	+	0.0236065i	−0.479417	+	0.877587i	$0.659152\pi$
$504$		0			0
$505$	4.16041	−	15.5268i	0.185136	−	0.690936i
$506$	−4.25947	+	2.45920i	−0.189356	+	0.109325i
$507$	6.62432	−	4.98544i	0.294196	−	0.221411i
$508$	−3.18576	+	5.51790i	−0.141345	+	0.244817i
$509$	10.8606	−	2.91008i	0.481387	−	0.128987i	−0.00996149	−	0.999950i	$-0.503171\pi$
$509$	10.8606	−	2.91008i	0.481387	−	0.128987i	0.491348	+	0.870963i	$0.336504\pi$
$510$	−11.1386	+	6.43089i	−0.493227	+	0.284765i
$511$		0			0
$512$	−1.18017	+	1.18017i	−0.0521565	+	0.0521565i
$513$	7.08184	−	7.08184i	0.312671	−	0.312671i
$514$	−27.0212	−	7.24032i	−1.19186	−	0.319357i
$515$	20.0748	−	5.37903i	0.884601	−	0.237028i
$516$			0.446140i			0.0196402i
$517$	1.50646	+	2.60927i	0.0662541	+	0.114755i
$518$		0			0
$519$		−	6.06965i		−	0.266428i
$520$	0.878691	+	14.4388i	0.0385332	+	0.633185i
$521$	14.6510	+	8.45874i	0.641871	+	0.370584i	0.785335	−	0.619071i	$-0.212491\pi$
$521$	14.6510	+	8.45874i	0.641871	+	0.370584i	−0.143464	+	0.989656i	$0.545824\pi$
$522$	22.4799	−	22.4799i	0.983917	−	0.983917i
$523$	−0.268849	−	0.155220i	−0.0117560	−	0.00678731i	0.494111	−	0.869399i	$-0.335494\pi$
$523$	−0.268849	−	0.155220i	−0.0117560	−	0.00678731i	−0.505866	+	0.862612i	$0.668827\pi$
$524$	8.07621	−	13.9884i	0.352811	−	0.611086i
$525$		0			0
$526$	−4.12779	−	15.4051i	−0.179980	−	0.671695i
$527$	36.5750	+	36.5750i	1.59323	+	1.59323i
$528$	−0.804367	−	3.00194i	−0.0350056	−	0.130643i
$529$	−7.03308	−	12.1816i	−0.305786	−	0.529637i
$530$	−10.6546	+	18.4543i	−0.462806	+	0.801603i
$531$	1.27455	+	0.341514i	0.0553106	+	0.0148204i
$532$		0			0
$533$	−9.24224	−	8.18188i	−0.400326	−	0.354396i
$534$	4.28959	+	7.42978i	0.185629	+	0.321518i
$535$	−18.5526	−	18.5526i	−0.802099	−	0.802099i
$536$	−1.71045			−0.0738803
$537$	3.83100			0.165320
$538$	0.377635	+	0.377635i	0.0162810	+	0.0162810i
$539$		0			0
$540$	5.60519	−	1.50190i	0.241209	−	0.0646317i
$541$	−8.05676	+	30.0682i	−0.346387	+	1.29273i	0.544597	+	0.838698i	$0.316683\pi$
$541$	−8.05676	+	30.0682i	−0.346387	+	1.29273i	−0.890984	+	0.454036i	$0.849984\pi$
$542$	−38.9581	+	22.4925i	−1.67340	+	0.966135i
$543$		−	3.86450i		−	0.165842i
$544$	6.70465	+	25.0221i	0.287459	+	1.07281i
$545$	23.5396			1.00833
$546$		0			0
$547$	−13.8672			−0.592920			−0.296460	−	0.955045i	$-0.595806\pi$
$547$	−13.8672			−0.592920			−0.296460	+	0.955045i	$0.595806\pi$
$548$	−2.25234	−	8.40583i	−0.0962150	−	0.359079i
$549$		−	33.7862i		−	1.44196i
$550$	1.36656	−	0.788983i	0.0582702	−	0.0336423i
$551$	5.31504	−	19.8360i	0.226428	−	0.845042i
$552$	−3.67475	+	0.984647i	−0.156408	+	0.0419094i
$553$		0			0
$554$	−17.9574	−	17.9574i	−0.762936	−	0.762936i
$555$	−6.14927			−0.261022
$556$	−13.1846			−0.559150
$557$	−16.0453	−	16.0453i	−0.679860	−	0.679860i	0.280108	−	0.959968i	$-0.409630\pi$
$557$	−16.0453	−	16.0453i	−0.679860	−	0.679860i	−0.959968	+	0.280108i	$0.909630\pi$
$558$	−18.7804	−	32.5286i	−0.795038	−	1.37705i
$559$	2.59959	−	1.71949i	0.109951	−	0.0727266i
$560$		0			0
$561$	−3.62003	−	0.969985i	−0.152838	−	0.0409528i
$562$	6.40703	−	11.0973i	0.270264	−	0.468111i
$563$	−11.2217	−	19.4366i	−0.472940	−	0.819156i	0.526580	−	0.850125i	$-0.323474\pi$
$563$	−11.2217	−	19.4366i	−0.472940	−	0.819156i	−0.999520	+	0.0309690i	$0.990141\pi$
$564$	−0.409927	−	1.52987i	−0.0172610	−	0.0644190i
$565$	11.5350	+	11.5350i	0.485283	+	0.485283i
$566$	−0.777562	−	2.90190i	−0.0326834	−	0.121976i
$567$		0			0
$568$	−11.6100	+	20.1090i	−0.487143	+	0.843756i
$569$	11.1921	+	6.46175i	0.469196	+	0.270891i	0.715903	−	0.698200i	$-0.246015\pi$
$569$	11.1921	+	6.46175i	0.469196	+	0.270891i	−0.246707	+	0.969090i	$0.579349\pi$
$570$	4.26602	−	4.26602i	0.178684	−	0.178684i
$571$	15.1053	+	8.72106i	0.632138	+	0.364965i	0.781580	−	0.623805i	$-0.214414\pi$
$571$	15.1053	+	8.72106i	0.632138	+	0.364965i	−0.149442	+	0.988771i	$0.547748\pi$
$572$	1.89880	−	2.14488i	0.0793928	−	0.0896821i
$573$			13.7928i			0.576202i
$574$		0			0
$575$	−1.43312	−	2.48223i	−0.0597650	−	0.103516i
$576$			6.93292i			0.288872i
$577$	−13.9338	+	3.73355i	−0.580071	+	0.155430i	−0.536912	−	0.843639i	$-0.680409\pi$
$577$	−13.9338	+	3.73355i	−0.580071	+	0.155430i	−0.0431598	+	0.999068i	$0.513742\pi$
$578$	30.4813	+	8.16745i	1.26786	+	0.339721i
$579$	−4.37022	+	4.37022i	−0.181620	+	0.181620i
$580$	8.41357	−	8.41357i	0.349354	−	0.349354i
$581$		0			0
$582$	−11.5729	+	6.68160i	−0.479711	+	0.276961i
$583$	−5.99760	+	1.60705i	−0.248395	+	0.0665573i
$584$	−1.45361	+	2.51772i	−0.0601507	+	0.104184i
$585$	−14.0737	−	12.4590i	−0.581874	−	0.515116i
$586$	−38.4555	+	22.2023i	−1.58858	+	0.917167i
$587$	−4.97130	+	18.5532i	−0.205188	+	0.765771i	0.784205	+	0.620502i	$0.213071\pi$
$587$	−4.97130	+	18.5532i	−0.205188	+	0.765771i	−0.989392	+	0.145268i	$0.953595\pi$
$588$		0			0
$589$	−21.0120	−	12.1313i	−0.865783	−	0.499860i
$590$	1.65596	+	0.443713i	0.0681748	+	0.0182674i
$591$	0.764402	−	2.85279i	0.0314433	−	0.117348i
$592$	−6.16199	+	22.9969i	−0.253256	+	0.945165i
$593$	2.51561	+	0.674056i	0.103304	+	0.0276802i	0.310101	−	0.950704i	$-0.399637\pi$
$593$	2.51561	+	0.674056i	0.103304	+	0.0276802i	−0.206797	+	0.978384i	$0.566304\pi$
$594$	5.08337	+	2.93489i	0.208573	+	0.120420i
$595$		0			0
$596$	−3.91804	+	14.6223i	−0.160489	+	0.598954i
$597$	11.9078	−	6.87500i	0.487356	−	0.281375i
$598$	−13.5246	−	11.9729i	−0.553063	−	0.489610i
$599$	−12.4050	+	21.4861i	−0.506855	+	0.877898i	0.493114	+	0.869965i	$0.335859\pi$
$599$	−12.4050	+	21.4861i	−0.506855	+	0.877898i	−0.999969	+	0.00793343i	$0.997475\pi$
$600$	1.17896	−	0.315903i	0.0481310	−	0.0128967i
$601$	−15.2889	+	8.82708i	−0.623649	+	0.360064i	−0.778288	−	0.627907i	$-0.783912\pi$
$601$	−15.2889	+	8.82708i	−0.623649	+	0.360064i	0.154639	+	0.987971i	$0.450578\pi$
$602$		0			0
$603$	1.57155	−	1.57155i	0.0639987	−	0.0639987i
$604$	−0.0208490	+	0.0208490i	−0.000848334	+	0.000848334i
$605$	19.4876	+	5.22168i	0.792282	+	0.212291i
$606$	−8.25620	+	2.21224i	−0.335385	+	0.0898662i
$607$		−	15.0740i		−	0.611835i	−0.952058	−	0.305917i	$-0.901037\pi$
$607$		−	15.0740i		−	0.611835i	0.952058	−	0.305917i	$-0.0989631\pi$
$608$	−6.07556	−	10.5232i	−0.246397	−	0.426771i
$609$		0			0
$610$		−	43.8969i		−	1.77733i
$611$	−7.33438	+	8.28491i	−0.296717	+	0.335172i
$612$	−10.8786	−	6.28074i	−0.439740	−	0.253884i
$613$	−24.8050	+	24.8050i	−1.00186	+	1.00186i	−0.00186450	+	0.999998i	$0.500593\pi$
$613$	−24.8050	+	24.8050i	−1.00186	+	1.00186i	−0.999998	+	0.00186450i	$0.999407\pi$
$614$	−3.17585	−	1.83358i	−0.128167	−	0.0739972i
$615$	2.19449	−	3.80097i	0.0884904	−	0.153270i
$616$		0			0
$617$	9.01921	+	33.6601i	0.363100	+	1.35511i	0.869979	+	0.493089i	$0.164132\pi$
$617$	9.01921	+	33.6601i	0.363100	+	1.35511i	−0.506879	+	0.862017i	$0.669201\pi$
$618$	−7.81429	−	7.81429i	−0.314337	−	0.314337i
$619$	2.05655	+	7.67515i	0.0826597	+	0.308490i	0.994861	−	0.101253i	$-0.0322851\pi$
$619$	2.05655	+	7.67515i	0.0826597	+	0.308490i	−0.912201	+	0.409743i	$0.865618\pi$
$620$	−7.02896	−	12.1745i	−0.282290	−	0.488940i
$621$	5.33095	−	9.23348i	0.213924	−	0.370527i
$622$	−47.4915	−	12.7253i	−1.90423	−	0.510238i
$623$		0			0
$624$	9.51949	−	6.29663i	0.381084	−	0.252067i
$625$	−9.64286	−	16.7019i	−0.385715	−	0.668077i
$626$	−33.1665	−	33.1665i	−1.32560	−	1.32560i
$627$	1.75795			0.0702056
$628$	−5.81741			−0.232140
$629$	20.3011	+	20.3011i	0.809460	+	0.809460i
$630$		0			0
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.677559	−	0.735469i	$-0.263038\pi$
$631$	40.9973	−	10.9852i	1.63208	−	0.437314i	0.954517	+	0.298155i	$0.0963713\pi$
$632$	5.99339	−	22.3676i	0.238404	−	0.889737i
$633$	−8.16866	+	4.71618i	−0.324675	+	0.187451i
$634$			13.1816i			0.523507i
$635$	4.09642	+	15.2880i	0.162561	+	0.606687i
$636$	3.26404			0.129428
$637$		0			0
$638$	12.0357			0.476497
$639$	−7.80890	−	29.1432i	−0.308915	−	1.15289i
$640$			26.4076i			1.04385i
$641$	17.7415	−	10.2431i	0.700748	−	0.404577i	−0.106878	−	0.994272i	$-0.534085\pi$
$641$	17.7415	−	10.2431i	0.700748	−	0.404577i	0.807626	+	0.589695i	$0.200752\pi$
$642$	−3.61088	+	13.4760i	−0.142510	+	0.531855i
$643$	20.9593	−	5.61604i	0.826556	−	0.221475i	0.179345	−	0.983786i	$-0.442602\pi$
$643$	20.9593	−	5.61604i	0.826556	−	0.221475i	0.647211	+	0.762311i	$0.275935\pi$
$644$		0			0
$645$	0.783647	+	0.783647i	0.0308561	+	0.0308561i
$646$	−28.1676			−1.10824
$647$	39.1337			1.53850			0.769252	−	0.638945i	$-0.220629\pi$
$647$	39.1337			1.53850			0.769252	+	0.638945i	$0.220629\pi$
$648$	−7.76875	−	7.76875i	−0.305185	−	0.305185i
$649$	0.249772	+	0.432618i	0.00980440	+	0.0169817i
$650$	4.33908	+	3.84126i	0.170193	+	0.150666i
$651$		0			0
$652$	12.8630	+	3.44664i	0.503755	+	0.134981i
$653$	14.8092	−	25.6503i	0.579528	−	1.00377i	−0.416005	−	0.909362i	$-0.636570\pi$
$653$	14.8092	−	25.6503i	0.579528	−	1.00377i	0.995533	−	0.0944103i	$-0.0300966\pi$
$654$	−6.25845	−	10.8400i	−0.244725	−	0.423876i
$655$	−10.3848	−	38.7566i	−0.405768	−	1.51435i
$656$	−12.0157	−	12.0157i	−0.469135	−	0.469135i
$657$	−0.977702	−	3.64883i	−0.0381438	−	0.142355i
$658$		0			0
$659$	1.87682	−	3.25074i	0.0731104	−	0.126631i	−0.827153	−	0.561977i	$-0.810041\pi$
$659$	1.87682	−	3.25074i	0.0731104	−	0.126631i	0.900263	+	0.435346i	$0.143374\pi$
$660$	0.882106	+	0.509284i	0.0343359	+	0.0198239i
$661$	−30.7260	+	30.7260i	−1.19510	+	1.19510i	−0.219487	+	0.975615i	$0.570438\pi$
$661$	−30.7260	+	30.7260i	−1.19510	+	1.19510i	−0.975615	+	0.219487i	$0.929562\pi$
$662$	−23.6341	−	13.6452i	−0.918566	−	0.530334i
$663$	−0.836048	−	13.7381i	−0.0324694	−	0.533544i
$664$			3.49363i			0.135579i
$665$		0			0
$666$	−10.4242	−	18.0552i	−0.403928	−	0.699623i
$667$		−	21.8617i		−	0.846488i
$668$	5.25482	−	1.40802i	0.203315	−	0.0544781i
$669$	13.1517	+	3.52399i	0.508475	+	0.136245i
$670$	2.04185	−	2.04185i	0.0788835	−	0.0788835i
$671$	9.04453	−	9.04453i	0.349160	−	0.349160i
$672$		0			0
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.0186390	−	0.999826i	$-0.494067\pi$
$673$	23.1880	−	13.3876i	0.893833	−	0.516055i	0.875194	+	0.483771i	$0.160733\pi$
$674$	17.8271	−	4.77675i	0.686673	−	0.183993i
$675$	−1.71032	+	2.96236i	−0.0658303	+	0.114021i
$676$	9.68143	+	4.11651i	0.372363	+	0.158327i
$677$	18.0711	−	10.4333i	0.694527	−	0.400985i	−0.110779	−	0.993845i	$-0.535334\pi$
$677$	18.0711	−	10.4333i	0.694527	−	0.400985i	0.805306	+	0.592860i	$0.202001\pi$
$678$	2.24506	−	8.37867i	0.0862209	−	0.321781i
$679$		0			0
$680$	20.7971	+	12.0072i	0.797532	+	0.460456i
$681$	−8.32680	−	2.23116i	−0.319084	−	0.0854982i
$682$	3.68038	−	13.7354i	0.140929	−	0.525954i
$683$	8.48852	−	31.6796i	0.324804	−	1.21219i	−0.589704	−	0.807619i	$-0.700756\pi$
$683$	8.48852	−	31.6796i	0.324804	−	1.21219i	0.914509	−	0.404567i	$-0.132578\pi$
$684$	5.69143	+	1.52501i	0.217617	+	0.0583103i
$685$	−18.7211	−	10.8087i	−0.715298	−	0.412977i
$686$		0			0
$687$	−1.18712	+	4.43039i	−0.0452914	+	0.169030i
$688$	3.71593	−	2.14539i	0.141668	−	0.0817923i
$689$	−12.5801	−	19.0191i	−0.479264	−	0.724570i
$690$	3.21130	−	5.56214i	0.122252	−	0.211747i
$691$	43.4491	−	11.6421i	1.65288	−	0.442888i	0.692464	−	0.721453i	$-0.256525\pi$
$691$	43.4491	−	11.6421i	1.65288	−	0.442888i	0.960418	+	0.278564i	$0.0898586\pi$
$692$	6.67003	−	3.85094i	0.253556	−	0.146391i
$693$		0			0
$694$	−5.60257	+	5.60257i	−0.212671	+	0.212671i
$695$	−23.1588	+	23.1588i	−0.878463	+	0.878463i
$696$	8.99236	+	2.40950i	0.340855	+	0.0913317i
$697$	−19.7934	+	5.30361i	−0.749727	+	0.200889i
$698$		−	38.9298i		−	1.47352i
$699$	−7.39940	−	12.8161i	−0.279871	−	0.484751i
$700$		0			0
$701$			38.7293i			1.46279i	0.681956	+	0.731393i	$0.261129\pi$
$701$			38.7293i			1.46279i	−0.681956	+	0.731393i	$0.738871\pi$
$702$	−4.30417	+	21.1226i	−0.162450	+	0.797223i
$703$	−11.6628	−	6.73352i	−0.439871	−	0.253960i
$704$	−1.85593	+	1.85593i	−0.0699482	+	0.0699482i
$705$	−3.40726	−	1.96718i	−0.128325	−	0.0740884i
$706$	11.0210	−	19.0889i	0.414780	−	0.718420i
$707$		0			0
$708$	−0.0679660	−	0.253653i	−0.00255432	−	0.00953285i
$709$	20.8624	+	20.8624i	0.783504	+	0.783504i	0.980420	−	0.196917i	$-0.0630928\pi$
$709$	20.8624	+	20.8624i	0.783504	+	0.783504i	−0.196917	+	0.980420i	$0.563093\pi$
$710$	−10.1457	−	37.8644i	−0.380763	−	1.42103i
$711$	15.0446	+	26.0580i	0.564215	+	0.977250i
$712$	8.00915	−	13.8723i	0.300156	−	0.519885i
$713$	−24.9490	−	6.68507i	−0.934348	−	0.250358i
$714$		0			0
$715$	−0.432246	−	7.10276i	−0.0161651	−	0.265628i
$716$	2.43061	+	4.20994i	0.0908362	+	0.157333i
$717$	−1.76849	−	1.76849i	−0.0660455	−	0.0660455i
$718$	−15.7559			−0.588003
$719$	8.46228			0.315590			0.157795	−	0.987472i	$-0.449562\pi$
$719$	8.46228			0.315590			0.157795	+	0.987472i	$0.449562\pi$
$720$	−18.2970	−	18.2970i	−0.681888	−	0.681888i
$721$		0			0
$722$	−17.9981	+	4.82258i	−0.669820	+	0.179478i
$723$	0.526386	−	1.96450i	0.0195765	−	0.0730605i
$724$	4.24676	−	2.45187i	0.157830	−	0.0911229i
$725$			7.01385i			0.260488i
$726$	−2.77656	−	10.3623i	−0.103048	−	0.384580i
$727$	−3.27056			−0.121299			−0.0606493	−	0.998159i	$-0.519317\pi$
$727$	−3.27056			−0.121299			−0.0606493	+	0.998159i	$0.519317\pi$
$728$		0			0
$729$	7.45103			0.275964
$730$	−1.27028	−	4.74076i	−0.0470153	−	0.175463i
$731$		−	5.17425i		−	0.191376i
$732$	−5.82309	+	3.36196i	−0.215228	+	0.124262i
$733$	−3.57318	+	13.3353i	−0.131979	+	0.492551i	−0.999992	−	0.00399003i	$-0.998730\pi$
$733$	−3.57318	+	13.3353i	−0.131979	+	0.492551i	0.868014	+	0.496541i	$0.165397\pi$
$734$	11.8502	−	3.17526i	0.437400	−	0.117201i
$735$		0			0
$736$	−9.14692	−	9.14692i	−0.337160	−	0.337160i
$737$	0.841407			0.0309936
$738$	14.8803			0.547750
$739$	30.0608	+	30.0608i	1.10580	+	1.10580i	0.993696	+	0.112109i	$0.0357605\pi$
$739$	30.0608	+	30.0608i	1.10580	+	1.10580i	0.112109	+	0.993696i	$0.464240\pi$
$740$	−3.90146	−	6.75753i	−0.143420	−	0.248412i
$741$	2.04666	+	6.12305i	0.0751861	+	0.224936i
$742$		0			0
$743$	−47.1919	−	12.6450i	−1.73130	−	0.463901i	−0.750820	−	0.660507i	$-0.770341\pi$
$743$	−47.1919	−	12.6450i	−1.73130	−	0.463901i	−0.980482	+	0.196606i	$0.937008\pi$
$744$	5.49953	−	9.52547i	0.201623	−	0.349221i
$745$	18.8021	+	32.5663i	0.688857	+	1.19314i
$746$	0.470729	+	1.75678i	0.0172346	+	0.0643204i
$747$	−3.20993	−	3.20993i	−0.117445	−	0.117445i
$748$	−1.23083	−	4.59352i	−0.0450036	−	0.167956i
$749$		0			0
$750$	−6.40223	+	11.0890i	−0.233776	+	0.404913i
$751$	9.96838	+	5.75525i	0.363751	+	0.210012i	0.670725	−	0.741706i	$-0.265983\pi$
$751$	9.96838	+	5.75525i	0.363751	+	0.210012i	−0.306974	+	0.951718i	$0.599316\pi$
$752$	−10.7711	+	10.7711i	−0.392782	+	0.392782i
$753$	6.51387	+	3.76078i	0.237379	+	0.137051i
$754$	14.0124	+	41.9211i	0.510300	+	1.52668i
$755$			0.0732428i			0.00266558i
$756$		0			0
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	0.655562	−	0.755141i	$-0.272432\pi$
$757$	−8.97468	−	15.5446i	−0.326190	−	0.564978i	−0.981753	+	0.190163i	$0.939098\pi$
$758$			43.6743i			1.58632i
$759$	1.80768	−	0.484368i	0.0656148	−	0.0175814i
$760$	−10.8806	−	2.91545i	−0.394681	−	0.105754i
$761$	7.83029	−	7.83029i	0.283848	−	0.283848i	−0.550794	−	0.834641i	$-0.685675\pi$
$761$	7.83029	−	7.83029i	0.283848	−	0.283848i	0.834641	+	0.550794i	$0.185675\pi$
$762$	5.95100	−	5.95100i	0.215582	−	0.215582i
$763$		0			0
$764$	−15.1571	+	8.75096i	−0.548365	+	0.316599i
$765$	−30.1404	+	8.07610i	−1.08973	+	0.291992i
$766$	−4.46711	+	7.73726i	−0.161403	+	0.279559i
$767$	−1.21604	+	1.37364i	−0.0439088	+	0.0495993i
$768$	9.20755	−	5.31598i	0.332249	−	0.191824i
$769$	2.87361	−	10.7245i	0.103625	−	0.386734i	−0.894561	−	0.446947i	$-0.852511\pi$
$769$	2.87361	−	10.7245i	0.103625	−	0.386734i	0.998186	+	0.0602130i	$0.0191780\pi$
$770$		0			0
$771$	9.21820	+	5.32213i	0.331986	+	0.191672i
$772$	−7.57523	−	2.02978i	−0.272638	−	0.0730533i
$773$	0.718001	−	2.67962i	0.0258247	−	0.0963792i	−0.951811	−	0.306686i	$-0.900780\pi$
$773$	0.718001	−	2.67962i	0.0258247	−	0.0963792i	0.977635	+	0.210307i	$0.0674464\pi$
$774$	−0.972476	+	3.62933i	−0.0349549	+	0.130454i
$775$	8.00436	+	2.14476i	0.287525	+	0.0770421i
$776$	21.6079	+	12.4753i	0.775678	+	0.447838i
$777$		0			0
$778$	−1.49192	+	5.56791i	−0.0534879	+	0.199619i
$779$	8.32421	−	4.80599i	0.298246	−	0.172192i
$780$	−0.746893	+	3.66537i	−0.0267431	+	0.131241i
$781$	5.71117	−	9.89204i	0.204362	−	0.353965i
$782$	−28.9646	+	7.76103i	−1.03577	+	0.277534i
$783$	−22.5949	+	13.0452i	−0.807477	+	0.466197i
$784$		0			0
$785$	−10.2183	+	10.2183i	−0.364707	+	0.364707i
$786$	−15.0864	+	15.0864i	−0.538113	+	0.538113i
$787$	−37.6817	−	10.0968i	−1.34321	−	0.359912i	−0.485585	−	0.874189i	$-0.661393\pi$
$787$	−37.6817	−	10.0968i	−1.34321	−	0.359912i	−0.857624	+	0.514278i	$0.828060\pi$
$788$	3.61995	−	0.969963i	0.128955	−	0.0345535i
$789$			6.06841i			0.216041i
$790$	19.5467	+	33.8559i	0.695441	+	1.20454i
$791$		0			0
$792$		−	5.08130i		−	0.180556i
$793$	42.0327	+	20.9728i	1.49262	+	0.744765i
$794$	0.872166	+	0.503545i	0.0309520	+	0.0178701i
$795$	5.73331	−	5.73331i	0.203340	−	0.203340i
$796$	15.1101	+	8.72381i	0.535563	+	0.309207i
$797$	16.0998	−	27.8857i	0.570285	−	0.987763i	−0.426251	−	0.904605i	$-0.640166\pi$
$797$	16.0998	−	27.8857i	0.570285	−	0.987763i	0.996536	−	0.0831583i	$-0.0265007\pi$
$798$		0			0
$799$	4.75426	+	17.7431i	0.168193	+	0.627707i
$800$	2.93459	+	2.93459i	0.103754	+	0.103754i
$801$	5.38699	+	20.1045i	0.190340	+	0.710358i
$802$	10.0498	+	17.4068i	0.354871	+	0.614655i
$803$	0.715059	−	1.23852i	0.0252339	−	0.0437064i
$804$	−0.427240	−	0.114479i	−0.0150676	−	0.00403735i
$805$		0			0
$806$	52.1261	−	3.17219i	1.83606	−	0.111736i
$807$	−0.101604	−	0.175984i	−0.00357664	−	0.00619492i
$808$	11.2848	+	11.2848i	0.396997	+	0.396997i
$809$	11.7932			0.414629			0.207314	−	0.978274i	$-0.433528\pi$
$809$	11.7932			0.414629			0.207314	+	0.978274i	$0.433528\pi$
$810$	18.5478			0.651705
$811$	−14.4330	−	14.4330i	−0.506811	−	0.506811i	0.406735	−	0.913546i	$-0.366667\pi$
$811$	−14.4330	−	14.4330i	−0.506811	−	0.506811i	−0.913546	+	0.406735i	$0.866667\pi$
$812$		0			0
$813$	16.5335	−	4.43015i	0.579856	−	0.155372i
$814$	2.04281	−	7.62388i	0.0716005	−	0.267217i
$815$	28.6480	−	16.5399i	1.00350	−	0.579369i
$816$		−	18.9477i		−	0.663302i
$817$	0.628174	+	2.34438i	0.0219770	+	0.0820194i
$818$	−19.4551			−0.680232
$819$		0			0
$820$	5.56926			0.194487
$821$	−2.34685	−	8.75856i	−0.0819056	−	0.305676i	0.912805	−	0.408396i	$-0.133912\pi$
$821$	−2.34685	−	8.75856i	−0.0819056	−	0.305676i	−0.994710	+	0.102721i	$0.967245\pi$
$822$			11.4947i			0.400925i
$823$	14.1019	−	8.14175i	0.491562	−	0.283804i	−0.233660	−	0.972318i	$-0.575070\pi$
$823$	14.1019	−	8.14175i	0.491562	−	0.283804i	0.725222	+	0.688515i	$0.241737\pi$
$824$	−5.34038	+	19.9306i	−0.186041	+	0.694314i
$825$	−0.579957	+	0.155399i	−0.0201915	+	0.00541030i
$826$		0			0
$827$	−27.1227	−	27.1227i	−0.943148	−	0.943148i	0.0553203	−	0.998469i	$-0.482382\pi$
$827$	−27.1227	−	27.1227i	−0.943148	−	0.943148i	−0.998469	+	0.0553203i	$0.982382\pi$
$828$	6.27265			0.217990
$829$	−2.81059			−0.0976158			−0.0488079	−	0.998808i	$-0.515542\pi$
$829$	−2.81059			−0.0976158			−0.0488079	+	0.998808i	$0.515542\pi$
$830$	−4.17051	−	4.17051i	−0.144760	−	0.144760i
$831$	4.83150	+	8.36841i	0.167603	+	0.290297i
$832$	−8.62510	−	4.30360i	−0.299021	−	0.149201i
$833$		0			0
$834$	16.8218	+	4.50738i	0.582490	+	0.156078i
$835$	6.75692	−	11.7033i	0.233833	−	0.405010i
$836$	1.11534	+	1.93183i	0.0385750	+	0.0668138i
$837$	7.97816	+	29.7749i	0.275765	+	1.02917i
$838$	−42.4077	−	42.4077i	−1.46495	−	1.46495i
$839$	9.79321	+	36.5488i	0.338099	+	1.26180i	0.900470	+	0.434918i	$0.143223\pi$
$839$	9.79321	+	36.5488i	0.338099	+	1.26180i	−0.562371	+	0.826885i	$0.690111\pi$
$840$		0			0
$841$	−12.2485	+	21.2150i	−0.422363	+	0.731553i
$842$	7.12836	+	4.11556i	0.245660	+	0.141832i
$843$	−3.44767	+	3.44767i	−0.118744	+	0.118744i
$844$	−10.3654	−	5.98444i	−0.356790	−	0.205993i
$845$	24.2362	−	9.77483i	0.833749	−	0.336264i
$846$		−	13.3389i		−	0.458602i
$847$		0			0
$848$	−15.6961	−	27.1864i	−0.539006	−	0.933586i
$849$			1.14312i			0.0392319i
$850$	9.29265	−	2.48996i	0.318735	−	0.0854049i
$851$	−13.8481	−	3.71058i	−0.474706	−	0.127197i
$852$	−4.24583	+	4.24583i	−0.145460	+	0.145460i
$853$	−7.88711	+	7.88711i	−0.270050	+	0.270050i	−0.829120	−	0.559070i	$-0.811158\pi$
$853$	−7.88711	+	7.88711i	−0.270050	+	0.270050i	0.559070	+	0.829120i	$0.311158\pi$
$854$		0			0
$855$	12.6757	−	7.31833i	0.433501	−	0.250282i
$856$	25.1612	−	6.74193i	0.859993	−	0.230434i
$857$	8.86465	−	15.3540i	0.302811	−	0.524483i	−0.673961	−	0.738767i	$-0.735408\pi$
$857$	8.86465	−	15.3540i	0.302811	−	0.524483i	0.976771	+	0.214284i	$0.0687417\pi$
$858$	−3.15588	+	2.08745i	−0.107740	+	0.0712643i
$859$	3.20832	−	1.85233i	0.109467	−	0.0632005i	−0.444267	−	0.895894i	$-0.646536\pi$
$859$	3.20832	−	1.85233i	0.109467	−	0.0632005i	0.553734	+	0.832694i	$0.313203\pi$
$860$	−0.363970	+	1.35835i	−0.0124113	+	0.0463195i
$861$		0			0
$862$	−0.712607	−	0.411424i	−0.0242715	−	0.0140132i
$863$	−38.0906	−	10.2063i	−1.29662	−	0.347428i	−0.456448	−	0.889750i	$-0.650879\pi$
$863$	−38.0906	−	10.2063i	−1.29662	−	0.347428i	−0.840171	+	0.542322i	$0.817545\pi$
$864$	−3.99561	+	14.9118i	−0.135933	+	0.507310i
$865$	4.95174	−	18.4801i	0.168364	−	0.628344i
$866$	28.7965	+	7.71601i	0.978546	+	0.262201i
$867$	−10.3986	−	6.00364i	−0.353155	−	0.203894i
$868$		0			0
$869$	−2.94827	+	11.0031i	−0.100013	+	0.373254i
$870$	−13.6109	+	7.85827i	−0.461454	+	0.266420i
$871$	0.979596	+	2.93068i	0.0331924	+	0.0993023i
$872$	−11.6853	+	20.2395i	−0.395713	+	0.685394i
$873$	−31.3155	+	8.39095i	−1.05987	+	0.283991i
$874$	12.1812	−	7.03283i	0.412036	−	0.237889i
$875$		0			0
$876$	−0.531592	+	0.531592i	−0.0179608	+	0.0179608i
$877$	−28.1504	+	28.1504i	−0.950570	+	0.950570i	−0.998835	−	0.0482643i	$-0.984631\pi$
$877$	−28.1504	+	28.1504i	−0.950570	+	0.950570i	0.0482643	+	0.998835i	$0.484631\pi$
$878$	46.3064	+	12.4078i	1.56277	+	0.418742i
$879$	16.3202	−	4.37298i	0.550467	−	0.147497i
$880$		−	9.79616i		−	0.330229i
$881$	1.49665	+	2.59227i	0.0504233	+	0.0873357i	0.890135	−	0.455696i	$-0.150610\pi$
$881$	1.49665	+	2.59227i	0.0504233	+	0.0873357i	−0.839712	+	0.543032i	$0.817276\pi$
$882$		0			0
$883$			1.38623i			0.0466504i	0.999728	+	0.0233252i	$0.00742531\pi$
$883$			1.38623i			0.0466504i	−0.999728	+	0.0233252i	$0.992575\pi$
$884$	14.5666	−	9.63502i	0.489927	−	0.324061i
$885$	−0.564925	−	0.326160i	−0.0189897	−	0.0109637i
$886$	8.73647	−	8.73647i	0.293508	−	0.293508i
$887$	−30.8094	−	17.7878i	−1.03448	−	0.597256i	−0.116214	−	0.993224i	$-0.537076\pi$
$887$	−30.8094	−	17.7878i	−1.03448	−	0.597256i	−0.918264	+	0.395968i	$0.870409\pi$
$888$	3.05254	−	5.28716i	0.102437	−	0.177425i
$889$		0			0
$890$	6.99906	+	26.1209i	0.234609	+	0.875573i
$891$	3.82161	+	3.82161i	0.128029	+	0.128029i
$892$	4.47166	+	16.6885i	0.149722	+	0.558771i
$893$	−4.30817	−	7.46197i	−0.144168	−	0.249705i
$894$	9.99780	−	17.3167i	0.334376	−	0.579157i
$895$	11.6642	+	3.12540i	0.389890	+	0.104471i
$896$		0			0
$897$	3.79166	+	5.73238i	0.126600	+	0.191398i
$898$	−19.5402	−	33.8446i	−0.652065	−	1.12941i
$899$	44.6931	+	44.6931i	1.49060	+	1.49060i
$900$	−2.01244			−0.0670815
$901$	−37.8558			−1.26116
$902$	3.98343	+	3.98343i	0.132634	+	0.132634i
$903$		0			0
$904$	−15.6439	+	4.19178i	−0.520310	+	0.139417i
$905$	3.15274	−	11.7662i	0.104801	−	0.391121i
$906$	0.0337282	−	0.0194730i	0.00112054	−	0.000646946i
$907$		−	49.8113i		−	1.65396i	−0.562233	−	0.826979i	$-0.690058\pi$
$907$		−	49.8113i		−	1.65396i	0.562233	−	0.826979i	$-0.309942\pi$
$908$	−2.83116	−	10.5660i	−0.0939553	−	0.350646i
$909$	−20.7368			−0.687795
$910$		0			0
$911$	−55.7036			−1.84554			−0.922772	−	0.385347i	$-0.874082\pi$
$911$	−55.7036			−1.84554			−0.922772	+	0.385347i	$0.874082\pi$
$912$	2.30033	+	8.58493i	0.0761714	+	0.284276i
$913$		−	1.71859i		−	0.0568769i
$914$	−6.54953	+	3.78137i	−0.216639	+	0.125077i
$915$	−4.32299	+	16.1336i	−0.142914	+	0.533360i
$916$	−5.62180	+	1.50636i	−0.185749	+	0.0497714i
$917$		0			0
$918$	25.3049	+	25.3049i	0.835187	+	0.835187i
$919$	−20.0645			−0.661867			−0.330934	−	0.943654i	$-0.607364\pi$
$919$	−20.0645			−0.661867			−0.330934	+	0.943654i	$0.607364\pi$
$920$	−11.9917			−0.395356
$921$	0.986663	+	0.986663i	0.0325116	+	0.0325116i
$922$	27.9203	+	48.3594i	0.919506	+	1.59263i
$923$	41.1038	+	8.37574i	1.35295	+	0.275691i
$924$		0			0
$925$	4.44286	+	1.19046i	0.146080	+	0.0391421i
$926$	34.4873	−	59.7338i	1.13332	−	1.96297i
$927$	−13.4054	−	23.2188i	−0.440290	−	0.762605i
$928$	8.19279	+	30.5759i	0.268942	+	1.00370i
$929$	22.3969	+	22.3969i	0.734818	+	0.734818i	0.971570	−	0.236752i	$-0.0760828\pi$
$929$	22.3969	+	22.3969i	0.734818	+	0.734818i	−0.236752	+	0.971570i	$0.576083\pi$
$930$	4.80595	+	17.9360i	0.157593	+	0.588146i
$931$		0			0
$932$	9.38923	−	16.2626i	0.307555	−	0.532700i
$933$	16.2016	+	9.35397i	0.530415	+	0.306235i
$934$	6.77600	−	6.77600i	0.221717	−	0.221717i
$935$	−10.2305	−	5.90659i	−0.334574	−	0.193166i
$936$	17.6985	−	5.91584i	0.578495	−	0.193365i
$937$			43.3600i			1.41651i	0.705957	+	0.708255i	$0.250517\pi$
$937$			43.3600i			1.41651i	−0.705957	+	0.708255i	$0.749483\pi$
$938$		0			0
$939$	8.92359	+	15.4561i	0.291210	+	0.504391i
$940$		−	4.99238i		−	0.162834i
$941$	37.4931	−	10.0463i	1.22224	−	0.327499i	0.410688	−	0.911776i	$-0.365289\pi$
$941$	37.4931	−	10.0463i	1.22224	−	0.327499i	0.811554	+	0.584277i	$0.198622\pi$
$942$	7.42224	+	1.98878i	0.241830	+	0.0647980i
$943$	7.23554	−	7.23554i	0.235622	−	0.235622i
$944$	−1.78586	+	1.78586i	−0.0581246	+	0.0581246i
$945$		0			0
$946$	−1.23190	+	0.711236i	−0.0400524	+	0.0231243i
$947$	−39.8444	+	10.6763i	−1.29477	+	0.346932i	−0.839470	−	0.543406i	$-0.817134\pi$
$947$	−39.8444	+	10.6763i	−1.29477	+	0.346932i	−0.455299	+	0.890339i	$0.650468\pi$
$948$	2.99408	−	5.18590i	0.0972431	−	0.168430i
$949$	5.14634	+	1.04867i	0.167057	+	0.0340413i
$950$	−3.90808	+	2.25633i	−0.126795	+	0.0732050i
$951$	1.29813	−	4.84468i	0.0420947	−	0.157100i
$952$		0			0
$953$	−9.00364	−	5.19825i	−0.291656	−	0.168388i	0.347032	−	0.937853i	$-0.387189\pi$
$953$	−9.00364	−	5.19825i	−0.291656	−	0.168388i	−0.638689	+	0.769465i	$0.720523\pi$
$954$	26.5529	+	7.11482i	0.859681	+	0.230351i
$955$	−11.2524	+	41.9947i	−0.364120	+	1.35892i
$956$	0.821387	−	3.06546i	0.0265655	−	0.0991439i
$957$	−4.42352	−	1.18528i	−0.142992	−	0.0383146i
$958$	−48.3721	−	27.9277i	−1.56283	−	0.902301i
$959$		0			0
$960$	0.887075	−	3.31061i	0.0286302	−	0.106850i
$961$	37.8246	−	21.8380i	1.22015	−	0.704452i
$962$	28.9328	−	1.76074i	0.932832	−	0.0567685i
$963$	−16.9235	+	29.3124i	−0.545353	+	0.944580i
$964$	2.49279	−	0.667940i	0.0802873	−	0.0215129i
$965$	−16.8713	+	9.74062i	−0.543105	+	0.313562i
$966$		0			0
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	−0.420775	−	0.907165i	$-0.638242\pi$
$967$	15.1251	−	15.1251i	0.486390	−	0.486390i	0.907165	+	0.420775i	$0.138242\pi$
$968$	−14.1634	+	14.1634i	−0.455228	+	0.455228i
$969$	10.3526	+	2.77396i	0.332572	+	0.0891124i
$970$	−40.6867	+	10.9020i	−1.30637	+	0.350041i
$971$			17.4624i			0.560396i	0.959942	+	0.280198i	$0.0904002\pi$
$971$			17.4624i			0.560396i	−0.959942	+	0.280198i	$0.909600\pi$
$972$	−5.75056	−	9.96026i	−0.184449	−	0.319475i
$973$		0			0
$974$		−	25.3407i		−	0.811968i
$975$	−1.21647	−	1.83911i	−0.0389583	−	0.0588986i
$976$	56.0040	+	32.3339i	1.79265	+	1.03498i
$977$	−8.45756	+	8.45756i	−0.270581	+	0.270581i	−0.829334	−	0.558753i	$-0.811280\pi$
$977$	−8.45756	+	8.45756i	−0.270581	+	0.270581i	0.558753	+	0.829334i	$0.311280\pi$
$978$	−15.2332	−	8.79490i	−0.487104	−	0.281230i
$979$	−3.93986	+	6.82405i	−0.125919	+	0.218097i
$980$		0			0
$981$	−7.85955	−	29.3322i	−0.250936	−	0.936506i
$982$	5.19914	+	5.19914i	0.165911	+	0.165911i
$983$	3.18140	+	11.8732i	0.101471	+	0.378695i	0.997921	−	0.0644501i	$-0.0205293\pi$
$983$	3.18140	+	11.8732i	0.101471	+	0.378695i	−0.896450	+	0.443145i	$0.853863\pi$
$984$	2.17872	+	3.77366i	0.0694551	+	0.120300i
$985$	4.65472	−	8.06222i	0.148312	−	0.256884i
$986$	70.8782	+	18.9918i	2.25722	+	0.604821i
$987$		0			0
$988$	−5.43019	+	6.13393i	−0.172757	+	0.195146i
$989$	1.29190	+	2.23763i	0.0410799	+	0.0711525i
$990$	6.06579	+	6.06579i	0.192783	+	0.192783i
$991$	−38.3547			−1.21838			−0.609189	−	0.793025i	$-0.708505\pi$
$991$	−38.3547			−1.21838			−0.609189	+	0.793025i	$0.708505\pi$
$992$	37.3991			1.18742
$993$	7.34257	+	7.34257i	0.233009	+	0.233009i
$994$		0			0
$995$	41.8644	−	11.2175i	1.32719	−	0.355619i
$996$	−0.233824	+	0.872644i	−0.00740901	+	0.0276508i
$997$	33.1334	−	19.1296i	1.04935	−	0.605840i	0.126879	−	0.991918i	$-0.459504\pi$
$997$	33.1334	−	19.1296i	1.04935	−	0.605840i	0.922466	+	0.386078i	$0.126171\pi$
$998$			33.5892i			1.06325i
$999$	4.42832	+	16.5267i	0.140106	+	0.522882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.80.2		32
7.2	even	3		637.2.bb.b.509.1		32
7.3	odd	6		91.2.bc.a.41.7	yes	32
7.4	even	3		91.2.bc.a.41.8	yes	32
7.5	odd	6		637.2.bb.b.509.2		32
7.6	odd	2	inner	637.2.x.b.80.1		32
13.7	odd	12		637.2.bb.b.423.2		32
21.11	odd	6		819.2.fm.g.496.2		32
21.17	even	6		819.2.fm.g.496.1		32
91.20	even	12		637.2.bb.b.423.1		32
91.33	even	12	inner	637.2.x.b.215.1		32
91.46	odd	12		91.2.bc.a.20.7	✓	32
91.59	even	12		91.2.bc.a.20.8	yes	32
91.72	odd	12	inner	637.2.x.b.215.2		32
273.59	odd	12		819.2.fm.g.748.2		32
273.137	even	12		819.2.fm.g.748.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.7	✓	32	91.46	odd	12
91.2.bc.a.20.8	yes	32	91.59	even	12
91.2.bc.a.41.7	yes	32	7.3	odd	6
91.2.bc.a.41.8	yes	32	7.4	even	3
637.2.x.b.80.1		32	7.6	odd	2	inner
637.2.x.b.80.2		32	1.1	even	1	trivial
637.2.x.b.215.1		32	91.33	even	12	inner
637.2.x.b.215.2		32	91.72	odd	12	inner
637.2.bb.b.423.1		32	91.20	even	12
637.2.bb.b.423.2		32	13.7	odd	12
637.2.bb.b.509.1		32	7.2	even	3
637.2.bb.b.509.2		32	7.5	odd	6
819.2.fm.g.496.1		32	21.17	even	6
819.2.fm.g.496.2		32	21.11	odd	6
819.2.fm.g.748.1		32	273.137	even	12
819.2.fm.g.748.2		32	273.59	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433802 - 1.61897i) q^{2} +0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(-0.520288 + 1.94174i) q^{5} +(1.03250 - 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +O(q^{10})\)	\(q+(-0.433802 - 1.61897i) q^{2} +0.637748i q^{3} +(-0.700831 + 0.404625i) q^{4} +(-0.520288 + 1.94174i) q^{5} +(1.03250 - 0.276656i) q^{6} +(-1.41124 - 1.41124i) q^{8} +2.59328 q^{9} +3.36932 q^{10} +(0.694217 + 0.694217i) q^{11} +(-0.258049 - 0.446954i) q^{12} +(-1.60977 + 3.22624i) q^{13} +(-1.23834 - 0.331813i) q^{15} +(-2.48181 + 4.29862i) q^{16} +(2.99281 + 5.18370i) q^{17} +(-1.12497 - 4.19844i) q^{18} +(-1.98532 - 1.98532i) q^{19} +(-0.421043 - 1.57135i) q^{20} +(0.822765 - 1.42507i) q^{22} +(-2.58851 - 1.49448i) q^{23} +(0.900016 - 0.900016i) q^{24} +(0.830467 + 0.479471i) q^{25} +(5.92151 + 1.20663i) q^{26} +3.56710i q^{27} +(3.65708 + 6.33425i) q^{29} +2.14878i q^{30} +(8.34708 - 2.23659i) q^{31} +(4.18037 + 1.12013i) q^{32} +(-0.442736 + 0.442736i) q^{33} +(7.09397 - 7.09397i) q^{34} +(-1.81745 + 1.04931i) q^{36} +(4.63309 - 1.24143i) q^{37} +(-2.35294 + 4.07541i) q^{38} +(-2.05753 - 1.02663i) q^{39} +(3.47451 - 2.00601i) q^{40} +(-0.886060 + 3.30682i) q^{41} +(-0.748633 - 0.432224i) q^{43} +(-0.767427 - 0.205631i) q^{44} +(-1.34925 + 5.03547i) q^{45} +(-1.29661 + 4.83903i) q^{46} +(2.96429 + 0.794280i) q^{47} +(-2.74144 - 1.58277i) q^{48} +(0.415990 - 1.55250i) q^{50} +(-3.30589 + 1.90866i) q^{51} +(-0.177238 - 2.91241i) q^{52} +(-3.16223 + 5.47715i) q^{53} +(5.77504 - 1.54742i) q^{54} +(-1.70918 + 0.986797i) q^{55} +(1.26614 - 1.26614i) q^{57} +(8.66852 - 8.66852i) q^{58} +(0.491481 + 0.131692i) q^{59} +(1.00213 - 0.268520i) q^{60} -13.0284i q^{61} +(-7.24196 - 12.5434i) q^{62} +2.67342i q^{64} +(-5.42698 - 4.80434i) q^{65} +(0.908836 + 0.524717i) q^{66} +(0.606011 - 0.606011i) q^{67} +(-4.19491 - 2.42193i) q^{68} +(0.953100 - 1.65082i) q^{69} +(-3.01121 - 11.2380i) q^{71} +(-3.65973 - 3.65973i) q^{72} +(-0.377014 - 1.40704i) q^{73} +(-4.01968 - 6.96230i) q^{74} +(-0.305782 + 0.529629i) q^{75} +(2.19469 + 0.588064i) q^{76} +(-0.769526 + 3.77644i) q^{78} +(5.80137 + 10.0483i) q^{79} +(-7.05555 - 7.05555i) q^{80} +5.50492 q^{81} +5.73802 q^{82} +(-1.23779 - 1.23779i) q^{83} +(-11.6225 + 3.11424i) q^{85} +(-0.374999 + 1.39951i) q^{86} +(-4.03966 + 2.33230i) q^{87} -1.95941i q^{88} +(2.07729 + 7.75255i) q^{89} +8.73759 q^{90} +2.41881 q^{92} +(1.42638 + 5.32334i) q^{93} -5.14367i q^{94} +(4.88792 - 2.82204i) q^{95} +(-0.714359 + 2.66602i) q^{96} +(-12.0756 + 3.23566i) q^{97} +(1.80030 + 1.80030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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